A MSVM demodulation method and computer program product for eLoran signals

Abstract

The present invention relates to a MSVM demodulation method and computer program product for eLoran signals. The method collects the first pulse signal of a received eLoran pulse group, analyzes the time domain characteristics of the eLoran signal, and extracts key eigenvectors. A training set is established based on the extracted eigenvectors and known modulation codewords. On this basis, a suitable kernel function and eigenvector selection method are selected to train the MSVM model. An optimization algorithm is used to find an optimal model that maintains high accuracy under various environments. The eigenvectors extracted in real time are input into the trained MSVM model. The model identifies and outputs the corresponding PPM modulation codeword based on the learned rules, completing the signal demodulation process. The MSVM demodulation algorithm proposed in the present invention can effectively extract signal features and train the model in different noise and interference environments, greatly improving the demodulation success rate of eLoran signals and having extremely high practical value in the design of eLoran receivers.

Description

Technical Field

[0001] The present invention belongs to the field of communications technology and relates to an MSVM demodulation method and computer program product for eLoran signals. Specifically, the present invention relates to a long-wave signal demodulation algorithm, a new MSVM (Multi-Support Vector Machine) demodulation algorithm for eLoran long-wave signals, and particularly a machine learning signal demodulation method for eLoran signal time-domain feature vectors based on the principle of a composite support vector machine. Background Art

[0002] As an internationally standardized ground-based radio system, the eLoran system provides PNT services with strong anti-interference capabilities and wide coverage. Its robust stability and excellent performance make it a promising and important supplement and backup system for GNSS systems. In recent years, many countries and regions around the world have initiated or re-initiated the development of the eLoran system. Demodulation and decoding are core modules in the eLoran system's signal reception and processing, directly impacting the implementation of timing functions and the accuracy of information transmission.

[0003] Accurately identifying the PPM modulation codewords of eLoran signals is the fundamental goal of demodulation technology. However, high levels of noise and continuous wave interference have always been challenges in ensuring demodulation accuracy. Currently, the most common demodulation technique used in eLoran receivers is envelope correlation detection. PPM modulation of the eLoran signal results in a phase offset of 0° or ±36°. This method compares the phase difference between the sampling point and the reference point, converting it into the corresponding modulation codeword. Decoding then yields the time code information.

[0004] However, this method inherently suffers from certain logical errors. Since the eLoran signal is amplitude modulated on a 100kHz carrier, and the carrier multiplication term between the ±1 modulated signal and the reference signal varies at each sampling point, even in an ideal, noise-free environment, the phase difference between each sampling point is not precisely 36°. Furthermore, the eLoran signal is highly susceptible to in-band continuous wave interference, which can cause phase difference fluctuations and increase the bit error rate.

[0005] Currently, there is limited research on demodulation methods for the eLoran system. Previous approaches using time-domain envelope correlation phase demodulation have been limited in their noise and interference resistance, severely limiting their use in eLoran receivers. First, noise can cause signal waveform distortion; second, strong in-band continuous wave interference can cause phase variations between the reference and detected signals. These factors can affect phase difference errors, leading to erroneous detection results and ultimately demodulation and decoding failures. This paper addresses these two inherent issues of the eLoran system by proposing a comprehensive demodulation solution based on a machine learning algorithm, significantly reducing the impact of noise and continuous wave interference. Summary of the Invention

[0006] Technical problems to be solved

[0007] In order to avoid the shortcomings of the existing technology, the present invention proposes an MSVM demodulation method and computer program product for eLoran signals, aiming to overcome the shortcomings of traditional demodulation technology in strong noise and continuous wave interference environments. In view of the characteristics of eLoran signals, this algorithm is based on the principle of support vector machine. It first performs signal acquisition and feature extraction to establish a training set for PPM modulation codeword recognition. By comparing different kernel functions and feature vector selections, the training process of the MSVM model is optimized to obtain an optimal demodulation model that can maintain high accuracy in harsh environments. Compared with the traditional envelope correlation detection method, the present invention uses machine learning technology to conduct in-depth analysis and processing of the time domain feature vectors of the eLoran signal, significantly improving the accuracy and stability of signal demodulation, especially in terms of anti-interference ability, providing strong technical support for the reliable operation of the eLoran system in various environments.

[0008] Technical Solution

[0009] An MSVM demodulation method for eLoran signals, characterized by the following steps:

[0010] Step 1: Pre-process the first pulse signal of the N received eLoran pulse groups by filtering and noise suppression.

[0011] Step 2: Perform time domain characteristic analysis on the pre-processed eLoran first pulse signal to extract the key feature vectors that characterize the PPM modulation characteristics of the signal;

[0012] Step 3: Use the extracted feature vectors and the set modulation codewords as the training set to train the MSVM model;

[0013] Step 4: Input the real-time extracted feature vector into the trained MSVM model to complete the signal demodulation process.

[0014] The pre-processing in step 1 is to use the BPF digital band-pass filtering method to filter the signal and perform noise and interference suppression processing.

[0015] The number of training samples in the training set is N=3n, where n is the number of eLoran pulse signals used for feature acquisition.

[0016] The key characteristic vectors that characterize the PPM modulation characteristics of the signal are: taking the pulse signal with the highest amplitude as the center, taking the positive and negative zero-crossing points, peak points, and positions 1us before and after the peak points of L consecutive sinusoidal carrier cycles, and collecting the values ​​of the same positions of the three forms of the first pulse of each pulse group.

[0017] The three modes are immediate, 1us ahead, and 1us behind.

[0018] The first L are 8.

[0019] The modulation code words set in the three forms are "+", "-", and "0".

[0020] The extracted feature vector combinations are: (1) using a 2L-dimensional vector of an approximate slope value; (2) using a 4L-dimensional vector combination of a 2L-dimensional approximate slope value and a 2L-dimensional zero-crossing position value; (3) using a 6L-dimensional vector combination of a 2L-dimensional approximate slope value, a 2L-dimensional zero-crossing position value, and a 2L-dimensional peak position value.

[0021] The kernel function used to train the MSVM model in step 3 is a linear kernel, a Gaussian kernel or a polynomial kernel.

[0022] A computer program product, characterized by comprising computer-executable instructions, wherein the instructions are used to implement the MSVM demodulation method for eLoran signals when executed.

[0023] Beneficial effects

[0024] The present invention proposes a MSVM demodulation method and computer program product for eLoran signals. First, the first pulse signal of N received eLoran pulse groups is collected and filtered and noise-suppressed by a preprocessing module to improve signal quality and facilitate subsequent feature extraction. Based on signal preprocessing, the time domain characteristics of the eLoran signal are analyzed to extract key eigenvectors. These eigenvectors effectively characterize the PPM modulation characteristics of the signal, providing the necessary input data for subsequent MSVM model training. A training set is established based on the extracted eigenvectors and known modulation codewords. Based on this, an appropriate kernel function and eigenvector selection method are selected to train the MSVM model. An optimization algorithm is used to find an optimal model that maintains high accuracy under various environments. The extracted eigenvectors are then input into the trained MSVM model. Based on the learned patterns, the model identifies and outputs the corresponding PPM modulation codewords, completing the signal demodulation process.

[0025] This invention addresses two major issues inherent in the eLoran system: signal waveform distortion caused by noise, and phase variations caused by strong in-band continuous wave interference on the reference and detected signals. These issues both contribute to phase difference errors, leading to erroneous detection results and ultimately to demodulation and decoding failures. This invention proposes a complete demodulation solution based on a machine learning algorithm, significantly reducing the impact of noise and continuous wave interference.

[0026] Numerous experiments have demonstrated that the proposed MSVM demodulation algorithm can effectively extract signal features and train models in diverse noise and interference environments, significantly improving the demodulation success rate of eLoran signals. This algorithm has high practical value in the design of eLoran receivers, providing a reliable guarantee for subsequent normal decoding and achieving high-precision PNT services. It can also provide a theoretical reference for the design and research of other related systems.

[0027] Based on the theory of Support Vector Machines (SVM), the present invention establishes an MSVM model that supports multi-classification problems based on the PPM modulation characteristics of eLoran signals. Secondly, based on the characteristics of eLoran pulse group signals, an appropriate feature vector extraction method is designed to successfully capture the effective signal characteristics and reduce the impact of waveform distortion caused by noise and irrelevant information on demodulation, providing a guarantee for the application of the present invention. Finally, the optimal model is obtained by comparing and designing different kernel functions, which greatly improves the demodulation performance of the eLoran system.

[0028] Based on the theory of SVM, the present invention establishes a composite support vector machine (MSVM) model to solve the multi-classification problem based on the PPM modulation characteristics of the eLoran signal. Secondly, according to the characteristics of the eLoran pulse group signal, an appropriate feature vector extraction method is designed to reduce the signal distortion and disturbance caused by noise and interference, providing a guarantee for the application of the present invention. Finally, by designing different kernel functions to optimize the selection design, the optimal model is obtained, which greatly improves the demodulation performance of the eLoran system. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is the overall block diagram of the algorithm of the present invention;

[0030] Figure 2 It is an available characteristic of the carrier period of the eLoran signal;

[0031] Figure 3 This is a schematic diagram of PPM modulation of the eLoran signal;

[0032] Figure 4 It is a comparison of DAR (demodulation accuracy rate) of different feature vector schemes in the MSVM algorithm;

[0033] Figure 5 It is the DAR comparison of different kernel function configurations in the MSVM algorithm;

[0034] Figure 6 This is the eLoran signal in a -5dB, 1-carrier interference environment;

[0035] Figure 7 The DAR curves and details of different demodulation methods without CWI are shown below;

[0036] Figure 8 It is a schematic diagram of the DAR curve of different demodulation methods when multiple carriers interfere. DETAILED DESCRIPTION

[0037] The present invention will now be further described with reference to the embodiments and drawings. The present invention includes but is not limited to the following embodiments.

[0038] The present invention provides a novel MSVM demodulation algorithm for eLoran signals, comprising the following steps:

[0039] Step 1, signal acquisition and preprocessing:

[0040] First, the first pulse signal of the received n eLoran pulse groups is collected, and the signal is filtered and subjected to noise and interference suppression using a BPF digital bandpass filter and other processing methods through the pre-processing module to improve the signal quality and create good conditions for subsequent feature extraction.

[0041] Here, n is the number of eLoran pulse signals used for feature acquisition. Since the first pulse of each pulse group of the eLoran signal is unmodulated, it can be collected as a known modulated signal and form a training set. A total of n groups are collected, and each signal is 1 ms long.

[0042] Step 2, feature extraction:

[0043] Based on signal preprocessing, key feature vectors are extracted from the signal. Feature extraction is based on the characteristic position points of the reference signal, including the positive and negative zero crossing points, peak points, and the positions 1us before and after the peak points of L high-amplitude carrier cycles of the signal. The values ​​of the same position are collected for three forms of the first pulse of each pulse group (immediate, 1us ahead, and 1us behind)

[0044] Specifically: taking the pulse signal with the highest amplitude as the center, take the positive and negative zero-crossing points, peak points, and the positions 1us before and after the peak points of L consecutive sinusoidal carrier cycles, and collect the values ​​of the same positions of the three forms of the first pulse of each pulse group.

[0045] The optimal number of training samples, N = 3n, is generally determined through a series of experiments. This ensures high model accuracy while maintaining reasonable computational cost. We conducted multiple experiments, increasing the number of sampled signals, n, from 50 to 500 in each set. The model accuracy and computation time were recorded for each set. The experimental results show that increasing n from 50 to 100 significantly improves model accuracy, while maintaining acceptable computational time. However, when n exceeds 100, the accuracy improvement becomes less pronounced and may even lead to the risk of overfitting, compromising model performance. However, the computational cost increases significantly. Considering the dual requirements of computational efficiency and accuracy in practical applications, we selected N = 300 samples, consisting of 100 sampled signals, as the training set size. This choice ensures demodulation performance while making model training and deployment feasible in resource-constrained environments.

[0046] For feature extraction, the L carrier cycles with the highest amplitudes are selected as the feature acquisition intervals, which is based on the fact that the power of these cycles is relatively strong, thereby reducing the impact of noise and interference to a certain extent and improving the reliability of the features. The present invention verifies through a series of experiments that the selection of these L carrier cycles in the dimension of the feature vector is carefully considered. In the experiment, we compared the features of different numbers of carrier cycles, including different configurations such as 6, 8, and 10, and evaluated the impact of each configuration on the demodulation performance of the MSVM model. The experimental results show that the feature configuration of 8 carrier cycles can provide the best performance balance in most cases, maintaining a high demodulation accuracy while avoiding the high computational complexity caused by too many features. In addition, we also found that although increasing or decreasing the number of peak points may bring a slight performance improvement under certain specific noise conditions, in general, the configuration of 8 carrier cycles can maintain stable performance in a wide range of noise and interference environments. Therefore, the present invention selects a configuration for feature sampling of L=8 carrier cycles. Specifically, for each pulse signal, 16 peak position point approximate slopes (positive and negative 1us sampling point value differences), 16 peak position point values, and 16 zero-crossing position point values ​​can be collected. Figure 2 shown.

[0047] Step 3, MSVM model training:

[0048] A training set was established using the extracted feature vectors and the corresponding known modulation codewords as labels. Based on this, three different SVM binary classification models were trained for the three-class eLoran signal demodulation problem using different kernel functions and feature vector selection methods. The optimal model was then compared and used to form the MSVM model.

[0049] Among them, the modulation code words are "+", "-", "0", such as Figure 3 As shown in the figure, the three labels correspond to the three forms of sampling the first pulse 1us behind, 1us ahead and immediate, and together with the high-dimensional feature vector constitute the training set.

[0050] In terms of feature vector selection, the present invention experimentally compares three different feature combination schemes to determine the optimal eLoran signal demodulation feature configuration, including: (1) using a 2L-dimensional vector of approximate slope values ​​(16 dimensions); (2) using a 4L-dimensional vector combination of 2L-dimensional approximate slope values ​​and 2L-dimensional zero-crossing position values ​​(32 dimensions); (3) using a 6L-dimensional vector combination of 2L-dimensional approximate slope values, 2L-dimensional zero-crossing position values, and 2L-dimensional peak position values ​​(48 dimensions).

[0051] According to different feature types, such as the combination of peak point position value and zero crossing point, etc. Experimental results (such as Figure 4(as shown) shows that scheme (3) achieves the highest demodulation accuracy. This finding emphasizes the great benefit of combining different feature types in the MSVM algorithm. By increasing the number and types of features, richer information can be provided to the learning process, thereby improving its performance. Table 2 provides a detailed statistical analysis of the DAR differences of these methods under different interference conditions. Scheme (3) shows significant performance advantages under various interference conditions, with an average DAR improvement of 3.36% to 4.93% over scheme (1). Under lower signal-to-noise ratio conditions (-20 to 0dB), this enhancement is more obvious, ranging from 4.91% to 7.92%. Therefore, scheme (3) was also selected as the feature vector combination scheme in the example.

[0052] Table 1 Average DAR (%) difference between each feature selection scheme in MSVM algorithm and scheme (1)

[0053]

[0054] Kernel function selection is also crucial in support vector machines. We experimentally compared the demodulation performance of different kernel functions, including common linear kernels, Gaussian kernels, and polynomial kernels. Experimental results show that the linear kernel consistently outperforms other kernel functions under various signal-to-noise ratio (SNR) and interference conditions. Within the SNR range of -20 to 10 dB, the average demodulation accuracy (DAR) is 0.71% to 5.73% higher than that of other kernel functions. This advantage becomes more pronounced with increasing interference. The linear kernel performs well in eLoran signal demodulation because it effectively captures the linear relationship in the signal and suppresses noise to a certain extent. In low SNR environments, the linear kernel reduces the impact of noise and improves model robustness by simplifying the feature map. In contrast, high-order polynomial kernels, while capable of handling complex nonlinear relationships, are prone to overfitting in noisy environments, affecting the model's generalization ability. Therefore, in this example, the linear kernel is selected as the optimal kernel function for the MSVM algorithm to achieve high-precision and robust eLoran signal demodulation.

[0055] Table 2 Statistics of the average DAR (%) difference between different kernel functions and linear kernel in MSVM algorithm

[0056]

[0057] Step 4, signal demodulation:

[0058] The corresponding feature vector is extracted from the signal to be tested and input into the trained MSVM model. The model will identify and output the corresponding PPM modulation codeword based on the learned rules, completing the signal demodulation process.

[0059] The distance between the sample and the hyperplane of each binary SVM classification model is calculated as the confidence score, and the data is classified and demodulated according to the high confidence principle.

[0060] This example uses three cases as examples to demonstrate the correctness and practicality of this method. The design conditions are as follows:

[0061] a. Bandpass filter: 95-105kHz; signal-to-noise ratio: -5dB white noise (before bandpass filtering); 1 carrier interference, interference frequency: 97.2222kHz, interference amplitude: 0.2; test message information: '1,1,1,12,30,0,24,2,15,0,0'.

[0062] b. Bandpass filter: 95-105kHz; signal-to-noise ratio: -20-10dB white noise (before bandpass filtering), 1dB step size; no continuous wave interference.

[0063] c. Bandpass filter: 95-105kHz; Signal-to-noise ratio: -20-10dB white noise (before bandpass filtering), 1dB step size; Number of carrier interferences: 2; Interference frequencies: 97.2222kHz, 101.3333kHz; Interference amplitudes: 0.2, 0.1; Interference initial phase: Random. Since the bandpass filter and the front-end interference removal module of the receiving terminal will eliminate most interference, set a moderate interference power.

[0064] According to the above settings, the specific process and results are as follows:

[0065] 1) The result under condition a:

[0066] According to the set interference environment, the signal and Figure 6 The example in [1] is similar. The time code information is modulated onto the eLoran signal, and the demodulation and decoding results are obtained through the receiving and processing flow.

[0067] Table 3 - Comparison of MSVM demodulation results and modulation information under 5dB white noise and 1 carrier interference environment

[0068] Pulse Group 1 2 3 4 5 6 7 8 9 10 Modulation Code 0-0+-+ +00+-- ++0--0 00+--+ 00-++- 00-00+ 00--++ 00--++ +0-+0- 0++--0 Demodulation Code 0-0+-+ +00+-- ++0--0 00+--+ 00-++- 00-00+ 00--++ 0+--++ +0-+0- 0++--0 Pulse Group 11 12 13 14 15 16 17 18 19 20 Modulation Code -+-++- 0-0++- +000-0 -+00-+ +0-+-0 0--0++ -+-00+ 00-+00 +0-000 0+0-+- Demodulation Code -+-++- 0-0++- +000-0 -+00-+ ++-+-0 0--0++ -+-00+ 00-+00 +0-000 0+0-+- Pulse Group 21 22 23 24 25 26 27 28 29 30 Modulation Code -0++-0 -+-0+0 0+-+-0 ++--00 -0+0-+ 0--++0 0-000+ 0+0-+- 0+0-00 0+0-00 Demodulation Code -0++-0 -+-0+0 0+-+-0 ++--00 -0+0-+ 00-++0 0-000+ 0+0-+- 0+0-00 0+0-00

[0069] The statistical results in Table 1 show that although the signal is severely distorted, there are only three errors in the 180 characters. Through the CRC-RS error correction decoding process, accurate time code information can be successfully obtained. These results also prove the correctness and feasibility of the MSVM algorithm for the demodulation and decoding problems of the eLoran system.

[0070] 2) Result under condition b:

[0071] Figure 7The DAR curves for various methods are shown. The statistics in Table 4 show that the performance of each method improves with increasing SNR. When the SNR is above -10 dB, the accuracy of each method exceeds 80%. ML algorithms, especially the MSVM algorithm, achieve the best demodulation performance, with DAR significantly outperforming the traditional EPD method. For example, at relatively low SNR levels, such as -20 dB, the DAR difference exceeds 20%, while the MSVM algorithm achieves 100% DAR above -2 dB.

[0072] 3) Result under condition c:

[0073] Depend on Figure 8 It is clear that the MSVM algorithm maintains optimal demodulation performance even in the presence of interference. As shown in Table 4, under two-carrier interference conditions, the MSVM algorithm's DAR is at least 12.87% higher than the EPD algorithm on average. This performance advantage is even more pronounced when there is no carrier interference, significantly outperforming other algorithms.

[0074] Table 4 Average DAR (%) difference between MSVM algorithm and EPD (other) algorithm.

[0075]

[0076] Figure 8 The results highlight the substantial negative impact of carrier interference on demodulation performance. Even in a high signal-to-noise ratio environment, high-intensity interference can severely degrade demodulation accuracy. Notably, at a signal-to-noise ratio of -10dB, the decoding success rate reaches a perfect score of 100%, demonstrating the superior performance of the MSVM algorithm compared to similar algorithms.

Claims

1. A MSVM demodulation method for eLoran signals, characterized in that Here are the steps: Step 1: Pre-process the first pulse signal of the n eLoran pulse groups received by filtering and noise suppression; Step 2: Perform time domain characteristic analysis on the pre-processed eLoran first pulse signal to extract the key feature vectors that characterize the PPM modulation characteristics of the signal; The key eigenvectors characterizing the PPM modulation characteristics of the signal are: taking the pulse signal with the highest amplitude as the center, taking the positive and negative zero-crossing points, peak points, and the positions 1us before and after the peak points of L consecutive sinusoidal carrier cycles, and collecting the values ​​of the same positions of the three forms of the first pulse of each pulse group; The three modes are immediate, 1us ahead, and 1us behind; Step 3: Use the extracted feature vectors and the set modulation codewords as the training set to train the MSVM model; Step 4: Input the real-time extracted feature vector into the trained MSVM model to complete the signal demodulation process.

2. The MSVM demodulation method for eLoran signals according to claim 1, wherein: The pre-processing in step 1 is to use the BPF digital band-pass filtering method to filter the signal and perform noise and interference suppression processing.

3. The MSVM demodulation method for eLoran signals according to claim 1, wherein: The number of training samples in the training set is N=3n, where n is the number of eLoran pulse signals used for feature acquisition.

4. The MSVM demodulation method for eLoran signals according to claim 1, wherein: The first L are 8.

5. The MSVM demodulation method for eLoran signals according to claim 1, wherein: The modulation code words corresponding to the three forms are "+", "-", and "0".

6. The MSVM demodulation method for eLoran signals according to claim 1, wherein: The extracted feature vector combinations are: (1) a 2L-dimensional vector using the approximate slope value; (2) a 4L-dimensional vector combination using a 2L-dimensional approximate slope value and a 2L-dimensional zero-crossing position value; and (3) a 6L-dimensional vector combination using a 2L-dimensional approximate slope value, a 2L-dimensional zero-crossing position value, and a 2L-dimensional peak position value.

7. The MSVM demodulation method for eLoran signals according to claim 1, wherein: The kernel function used to train the MSVM model in step 3 is a linear kernel, a Gaussian kernel or a polynomial kernel.

8. A computer program product, characterized in that The present invention comprises computer-executable instructions, which, when executed, are used to implement any one of the MSVM demodulation methods for eLoran signals described in claims 1 to 7.

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