A cold atom gravimeter frequency boosting method based on long short-term memory network-exponential moving average algorithm

Abstract

The application relates to a cold atom gravimeter frequency promotion method based on a long short-term memory network-exponential moving average algorithm, and relates to the fields of cold atom gravimeter measurement and the like. In order to solve the defects that the output frequency of a cold atom gravimeter is low and it is difficult to consider high precision and high frequency in the prior art, the technical scheme provided by the application comprises the following steps: acquiring original gravity acceleration data output by the cold atom gravimeter and obtaining denoised data; performing linear interpolation on the denoised data to generate a continuous input sequence for long short-term memory network training and prediction; outputting a next-time gravity acceleration prediction value according to the continuous input sequence; generating a frequency promotion sequence composed of measured data and predicted data according to the prediction value; and obtaining final high-frequency gravity acceleration output data. The application is suitable for work of obtaining high-precision and high-frequency gravity acceleration data in geological exploration, gravity matching navigation and geophysical monitoring.

Description

Technical Field

[0001] This research relates to fields such as cold atom gravimeter measurement, and in particular to a method for improving the frequency of cold atom gravimeters based on a long short-term memory network-exponential moving average algorithm. Background Technology

[0002] Gravitational acceleration is a crucial parameter that must be considered in many scientific research activities. For example, measuring the gravity field of a region and matching it with a gravity reference map in a gravity field database using a matching algorithm can enable gravity-matched navigation, correcting errors in inertial navigation. Measuring gravity values ​​near a volcano's crater allows us to infer the activity of magma and escaping gases within the volcano, thus facilitating geological exploration. Therefore, accurate measurement of gravitational acceleration is of great significance in basic scientific research, geological mapping, and national defense.

[0003] Cold atom gravimeters can accurately measure gravitational acceleration. They use atoms of some alkali metals, such as rubidium, as the quantum measurement medium. Through the preparation and confinement of cold atoms, their upward and free-fall processes, beam splitting-reflection-interference, and detection, gravitational acceleration is inverted by measuring the quantum phase changes of freely falling atoms in the gravitational field. The error is generally in μGal, i.e., 10⁻⁸ m / s². 2 To ensure accuracy, a sufficiently long interference time is needed for cold atoms during the beam splitting-reflection-interference process. Furthermore, the cooling and trapping of the atoms are also time-consuming. This results in a long measurement period for each gravitational acceleration value by the cold atom gravimeter, with measurement cycles reaching tens of seconds or even longer. This means there is a "dead zone" between the two output values. Within this dead zone, no gravity information can be obtained, severely impacting the measurement performance of the cold atom gravimeter.

[0004] Increasing the output frequency of a cold atom gravimeter can improve the measurement bandwidth, preventing insufficient data from failing to accurately capture changes in gravitational acceleration. This helps increase data density, enabling more detailed analysis of gravity signals, especially short-term gravity fluctuations; it also helps to more clearly reveal the details of the signal, allowing for a more nuanced understanding of the underlying causes of gravity changes and improving reliability in fields such as geological exploration; furthermore, it helps signal processing algorithms provide higher-quality input data, increasing the applicability of gravity data.

[0005] Currently, methods to increase the measurement frequency of cold atom gravimeters mainly include optimizing structural design and cascading equipment. The former improves the efficiency of gravity measurement by reducing the time spent on cold atom preparation and other processes, but requires complex structural design, and the sensitivity of gravity measurement gradually decreases as the output frequency increases. The latter improves measurement efficiency by cascading multiple cold atom gravimeters, allowing different devices to operate alternately. While this can increase the measurement frequency to tens of hertz, it requires the simultaneous installation of dozens of devices and the implementation of additional timing control algorithms to accurately monitor and control the operating status of each cold atom gravimeter, significantly increasing cost and complexity. In most practical applications, both optimized structural design and equipment cascading present considerable challenges in implementation.

[0006] In summary, existing technologies suffer from drawbacks such as low output frequency of cold atom gravimeters, high cost or complex implementation of traditional frequency enhancement methods, and difficulty in achieving both high precision and high frequency. Summary of the Invention

[0007] To address the shortcomings of existing technologies, such as low output frequency of cold atom gravimeters and high cost or complexity of traditional frequency enhancement methods, making it difficult to simultaneously achieve high precision and high frequency, the technical solution provided by this invention is as follows: A frequency enhancement method for cold atom gravimeters based on a long short-term memory network-exponential moving average algorithm includes: The steps include acquiring the raw gravitational acceleration data output by the cold atom gravimeter and performing a first exponential moving average smoothing process to obtain noise-reduced data. The step of performing linear interpolation on the denoised data to generate a continuous input sequence for training and prediction of the long short-term memory network; The steps are as follows: inputting the continuous input sequence into a long short-term memory network, learning data features, and outputting the predicted value of gravitational acceleration at the next moment; The step of inserting the predicted value between adjacent data of the noise reduction data to generate a frequency boosting sequence composed of the measured data and the predicted data; The step of performing a second exponential moving average smoothing process on the frequency-enhanced sequence to obtain the final high-frequency gravitational acceleration output data.

[0008] Furthermore, a preferred embodiment is provided in which the smoothing factor of the first exponential moving average smoothing process is less than five percent.

[0009] Furthermore, a preferred implementation is provided in which the continuous input sequence generated by linear interpolation covers the time interval between the original measured points.

[0010] Furthermore, a preferred implementation method is provided, in which the Long Short-Term Memory Network is used for learning and validation by dividing the training set and the test set in a ratio of nine to one.

[0011] Furthermore, a preferred embodiment is provided in which the predicted value is inserted between adjacent data of the noise-reduced data, thereby doubling the original frequency.

[0012] Furthermore, a preferred embodiment is provided in which the smoothing factor of the second exponential moving average smoothing process is greater than 50%.

[0013] A frequency enhancement device for cold atom gravimeters based on a long short-term memory network-exponential moving average algorithm is also provided, comprising: A module that acquires the raw gravitational acceleration data output by the cold atom gravimeter and performs the first exponential moving average smoothing process to obtain noise-reduced data. A module that performs linear interpolation on the denoised data to generate a continuous input sequence for training and prediction of the Long Short-Term Memory Network; The module that inputs the continuous input sequence into the long short-term memory network, learns the data features, and outputs the predicted value of the gravitational acceleration at the next moment; A module that inserts the predicted value between adjacent data of the noise reduction data to generate a frequency boost sequence composed of the measured data and the predicted data; A module that performs a second exponential moving average smoothing process on the frequency-enhanced sequence to obtain the final high-frequency gravitational acceleration output data.

[0014] A computer storage medium is also provided for storing a computer program, which, when read by the computer, executes the method.

[0015] A computer is also provided, including a processor and a storage medium, wherein the computer executes the method when the processor reads a computer program stored in the storage medium.

[0016] A computer program product is also provided, which, when executed, implements the method described.

[0017] Compared with the prior art, the advantages of the technical solution provided by the present invention are as follows: This scheme first uses an exponential moving average method to smooth the raw gravity acceleration measurement data before it enters the learning and prediction stage, effectively reducing noise interference in the signals acquired by the cold atom gravimeter. This step ensures that the data input into the long short-term memory network has good stability, avoiding negative impacts from noise on the model learning process and prediction accuracy. Compared with existing methods that directly input raw data, this method makes the subsequent prediction stage more stable and reliable.

[0018] This approach introduces linear interpolation into the data preprocessing, transforming the data after the initial smoothing into a continuous sequence that can be learned and predicted by the Long Short-Term Memory (LSTM) network. This method compensates for the "dead zone" in the time dimension of the original data, allowing the model to obtain continuous input even at time points where measured values ​​are lacking. Compared to traditional methods that rely solely on measured data for modeling, this approach enhances the model's ability to learn from changes in time series data.

[0019] This scheme utilizes a Long Short-Term Memory (LSTM) network to train and predict smoothed and interpolated sequences, thereby generating predicted values ​​for gravitational acceleration at future time points. LSM networks have the advantage of handling long-term dependencies, enabling them to better capture trends and details in gravity signals. Compared to common traditional regression or autoregressive models, this approach significantly improves prediction accuracy, ensuring that the frequency-enhanced data remains highly consistent with the actual physical signal.

[0020] This scheme, after obtaining the predicted data, inserts it between the measured data after the first smoothing process, forming a combined sequence of original and predicted data. This method effectively doubles the original measurement frequency, thereby significantly shortening the time interval between data outputs. Compared with existing methods that achieve frequency increase through hardware structure optimization or device cascading, this method requires no additional hardware modifications, relying solely on data processing algorithms to achieve frequency doubling, significantly reducing implementation costs.

[0021] This scheme applies an exponential moving average method for smoothing after the combined data is generated, thereby reducing sawtooth noise introduced by prediction errors and improving overall smoothness while preserving data signal details. This approach ensures the usability and stability of the output data, and compared to direct output without secondary smoothing, further reduces the root mean square error of the prediction data, thus improving data quality.

[0022] This scheme employs a complete process of "first smoothing—linear interpolation—long short-term memory network prediction—data merging—second smoothing," forming a purely algorithm-driven frequency enhancement method. Compared to existing technologies that rely on hardware modifications, this approach not only avoids interference with the core structure of the cold atom gravimeter but also improves the system's adaptability to various application scenarios, enabling a single device to meet the demand for high-frequency output.

[0023] It is suitable for work that requires high-precision and high-frequency gravity acceleration data in geological exploration, gravity matching navigation and geophysical monitoring. Attached Figure Description

[0024] Figure 1 The flowchart shows the frequency enhancement method for cold atom gravimeters based on the LSTM-EMA algorithm. Figure 2 This is a schematic diagram of the data flow during continuous operation of a cold atom gravimeter frequency enhancement method based on a long short-term memory network-exponential moving average algorithm. Figure 3 Comparison of the original gravity data with the first smoothing result; Figure 4 This is a comparison of the final output results, combined data, and control group. Detailed Implementation

[0025] To make the advantages and benefits of the technical solution provided by the present invention clearer, the technical solution provided by the present invention will now be described in further detail with reference to the accompanying drawings, specifically: Implementation Method 1: This implementation method provides a frequency enhancement method for cold atom gravimeters based on a long short-term memory network-exponential moving average algorithm, including: The steps include acquiring the raw gravitational acceleration data output by the cold atom gravimeter and performing a first exponential moving average smoothing process to obtain noise-reduced data. The step of performing linear interpolation on the denoised data to generate a continuous input sequence for training and prediction of the long short-term memory network; The steps are as follows: inputting the continuous input sequence into a long short-term memory network, learning data features, and outputting the predicted value of gravitational acceleration at the next moment; The step of inserting the predicted value between adjacent data of the noise reduction data to generate a frequency boosting sequence composed of the measured data and the predicted data; The step of performing a second exponential moving average smoothing process on the frequency-enhanced sequence to obtain the final high-frequency gravitational acceleration output data.

[0026] The smoothing factor for the first exponential moving average smoothing process is less than 5%.

[0027] The continuous input sequence generated by linear interpolation covers the time interval between the original measured points.

[0028] Long Short-Term Memory (LSTM) networks are used for learning and validation by dividing the training set and the test set in a 9:1 ratio.

[0029] The predicted value is inserted between adjacent data in the noise-reduced data, thereby doubling the original frequency.

[0030] The smoothing factor for the second exponential moving average smoothing process is greater than 50%.

[0031] Implementation Method Two: This implementation method is a further detailed description of the technical solution provided in Implementation Method One, specifically: The overall approach involves performing two smoothing processes on the raw gravitational acceleration data output by the cold atom gravimeter. During these smoothing processes, interpolation and a long short-term memory (LSTM) network prediction algorithm are combined to generate new predicted data, which is then integrated with the original data to increase the measurement frequency. The entire method includes the following steps: First, the raw gravitational acceleration data output by cold atom gravimeters typically contains noise components, such as those from optical system jitter, environmental disturbances, or probe noise. Directly using this data for model learning and prediction can easily lead to unstable or even distorted predictions. Therefore, in the first step of this method, an exponential moving average algorithm is used to smooth the raw data. The exponential moving average algorithm establishes a weighted relationship between current and historical data points, ensuring that historical data retains some influence in the smoothed sequence, thus effectively reducing the impact of high-frequency noise. The result is a smoothed data sequence with stronger trend and less noise, providing a reliable foundation for subsequent interpolation and prediction.

[0032] Next, to overcome the time "dead zone" problem caused by the long measurement cycle and sparse data output of the cold atom gravimeter, linear interpolation was performed on the data after the first smoothing process. Linear interpolation generates intermediate values ​​between measured points by establishing straight lines connecting adjacent data points, thus obtaining a more continuous sequence in the time dimension. This step not only improves the smoothness and coherence of the input sequence, but also provides a more uniform and complete training input for the Long Short-Term Memory network.

[0033] Based on the interpolated data, the generated training sequences are input into a Long Short-Term Memory (LSTM) network model for learning. LTM, through its unique gating unit structure, can remember long-term dependencies and suppress irrelevant information, making it particularly suitable for processing slowly changing time-series signals with complex trends, such as gravitational acceleration. During training, the model first learns the features of the input sequences using the training set, and then validates its performance using the test set to ensure good generalization ability. After training, the model can predict the gravitational acceleration value at the next moment based on the existing sequences, thus obtaining predictive data that complements the measured time locations.

[0034] Subsequently, the predicted gravitational acceleration values ​​are inserted between adjacent measured points in the first smoothing process, forming a combined data sequence composed of both measured and predicted data. This combined sequence is encrypted along the time axis, effectively doubling the output frequency of the original data. Compared to traditional methods that rely on hardware modifications or cascading multiple devices to increase frequency, this method achieves frequency doubling entirely based on data processing algorithms, without requiring additional hardware resources.

[0035] Since prediction data inevitably contains some error, the combined data may exhibit subtle sawtooth fluctuations. Using this data directly could affect the reliability of subsequent applications. Therefore, the combined data is again input into an exponential moving average algorithm for smoothing. By setting an appropriate smoothing factor, the fluctuations introduced by prediction errors can be reduced while preserving as much of the signal's detailed variation characteristics as possible. The final output data not only achieves encryption in the time dimension but also shows significant improvements in accuracy and stability.

[0036] Taking a specific experiment as an example, a gravitational acceleration sequence of 300 data points was obtained from a cold atom gravimeter. The maximum value of this sequence is 980,111,084.01 microgales, and the minimum value is 980,111,037.38 microgales. First, the data underwent unit conversion and normalization. Then, a first smoothing was performed using an exponential moving average algorithm with a smoothing factor of 1%, resulting in denoised EMA1 data. Next, a training sequence was constructed using linear interpolation, and the training and test sets were divided at a ratio of 9:1. This data was then input into a long short-term memory network model for training and prediction. After processing, 28 prediction points were generated, which, after inserting into the original data, formed a combined sequence of 56 points. Finally, a second smoothing was performed on the combined sequence using an exponential moving average algorithm with a smoothing factor of 75%, yielding the final output sequence. Experimental results show that the root mean square error of the combined data is 0.0426 microgales, while the root mean square error of the final output is 0.0377 microgales, representing an accuracy improvement of approximately 11.4%, fully validating the effectiveness of this implementation method.

[0037] Therefore, this implementation method, through two exponential moving average smoothing processes combined with linear interpolation and long short-term memory network prediction, effectively increases the data frequency of cold atom gravimeters without increasing hardware burden. It boasts advantages such as low cost, ease of implementation, and high stability, and can meet the high-frequency data requirements of fields such as geological exploration, gravity matching navigation, and geophysical monitoring. Implementation Method 3: Combination Figure 1-4 This embodiment describes the technical solution provided above in further detail through specific examples. Specifically: To address the issues of low output frequency of cold atom gravimeters and the difficulty in implementing existing frequency enhancement methods, this embodiment proposes a frequency enhancement method for cold atom gravimeters based on a Long Short-Term Memory Network (LSTM)-Exponential Moving Average (EMA) algorithm. The gravitational acceleration data measured by the cold atom gravimeter is smoothed using a first EMA, followed by linear interpolation to obtain a sequence for learning and prediction. Then, an LSTM prediction algorithm is used to predict a sequence of values ​​for frequency enhancement. Finally, the combined data undergoes a second EMA smoothing process, achieving frequency enhancement of the gravity data measurement.

[0038] The purpose of this embodiment is to provide a method for frequency enhancement of a cold atom gravimeter based on the LSTM-EMA algorithm, rather than traditional solutions such as changing the instrument design or adding additional equipment.

[0039] The technical solution to achieve the objective of this embodiment is: a method for frequency enhancement of a cold atom gravimeter based on the LSTM-EMA algorithm, comprising the following steps: Step 1: Noise reduction of raw gravitational acceleration measurement data; Step 2: Generate input data for LSTM model learning; Step 3: The LSTM model learns the features of the input data and predicts the gravitational acceleration data for the next moment based on the learning results; Step 4: Merge the original data and the data predicted by the LSTM model; Step 5: Perform a second round of smoothing and noise reduction on the merged data.

[0040] In step one, since the raw gravitational acceleration data collected by the cold atom gravimeter contains noise, in order to avoid the noise affecting the learning and prediction process of LSTM, the data is first subjected to EMA smoothing to generate noise-reduced data.

[0041] In step four, the gravitational acceleration value predicted in step three is inserted between the two corresponding data points obtained from the first smoothing process in step one, thus doubling the frequency of the original measurement data.

[0042] In step five, the same EMA smoothing algorithm as in step one is used again to reduce the jagged noise that may be caused by LSTM prediction errors.

[0043] Compared with the prior art, the beneficial effects of this embodiment are: Traditional methods mostly increase output frequency by shortening the cold atom preparation time or by cascading multiple devices. The former has a high technical threshold, while the latter involves extremely high costs for purchasing, installing, and maintaining multiple devices, resulting in significant limitations under current conditions in most application scenarios. In contrast, the software-based frequency upscaling method proposed in this embodiment completely eliminates the dependence on hardware modification, offering the following advantages: (1) Low implementation cost and strong feasibility: The method proposed in this embodiment does not require any modification to the hardware structure of the cold atom gravimeter. It only needs to integrate the corresponding software algorithm into the control system of the existing equipment to quickly realize the frequency enhancement function, which greatly reduces the threshold for using the cold atom gravimeter frequency enhancement method and effectively controls economic and time costs. (2) Good stability: The method proposed in this embodiment does not interfere with the working state of the cold atom gravimeter itself. It can avoid changing the original core structure design of the equipment, which would disrupt its working stability balance. It can also prevent the problem of data interference between different equipment due to timing control deviation when multiple equipment are cascaded, thus ensuring the accuracy and stability of the output data. (3) Strong adaptability: The method proposed in this embodiment can be well adapted to the operation mode of a single device. It only needs to rely on the existing gravity acceleration data output of a single cold atom gravimeter. Data processing and frequency enhancement can be achieved through algorithms, which can meet the usage needs of most application scenarios.

[0044] In a specific embodiment: To verify the effectiveness of this implementation method, a segment of cold atom gravimeter gravitational acceleration measurements with 300 data points was extracted. The unit of this data is μGal, with a maximum value of 980111084.01 μGal and a minimum value of 980111037.38 μGal. After unit conversion, the raw data underwent a first EMA smoothing process using a smoothing factor α=0.01 to minimize noise interference while preserving certain gravitational trend characteristics, ultimately obtaining EMA 1 data, as shown below. Figure 3 As shown.

[0045] The training and test sets were divided in a 9:1 ratio, with the training set used to train and predict the model. Due to the large range and uneven distribution of the data, normalization was used instead of the original data in this simulation. Finally, by recording starting from the second output value, 28 predicted values ​​of gravitational acceleration were obtained.

[0046] The algorithm in this embodiment can boost the output frequency of the cold atom gravimeter to twice the original frequency, thus generating a frequency boost sequence of 56 values ​​from 28 gravitational acceleration predictions.

[0047] The combined data is then subjected to a second EMA smoothing process to obtain the final output result, such as... Figure 4 As shown, due to the weak noise from the prediction error and the need to retain more data details, the smoothing factor α was set to 0.75 for the second EMA smoothing process. The root mean square error of the combined data was 0.0426 μGal, and the root mean square error of the final result was 0.0377 μGal. The second EMA smoothing algorithm improved the accuracy by 11.4%.

[0048] The above description of several specific embodiments further details the technical solution provided by the present invention in order to highlight the advantages and benefits of the technical solution provided by the present invention. However, the above-described specific embodiments are not intended to limit the present invention. Any reasonable modifications and improvements to the present invention, combinations of embodiments, and equivalent substitutions based on the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for frequency enhancement of cold atom gravimeters based on Long Short-Term Memory Network-Exponential Moving Average algorithm, characterized in that, include: The steps include acquiring the raw gravitational acceleration data output by the cold atom gravimeter and performing a first exponential moving average smoothing process to obtain noise-reduced data. The step of performing linear interpolation on the denoised data to generate a continuous input sequence for training and prediction of the long short-term memory network; The steps are as follows: inputting the continuous input sequence into a long short-term memory network, learning data features, and outputting the predicted value of gravitational acceleration at the next moment; The step of inserting the predicted value between adjacent data of the noise reduction data to generate a frequency boosting sequence composed of the measured data and the predicted data; The step of performing a second exponential moving average smoothing process on the frequency-enhanced sequence to obtain the final high-frequency gravitational acceleration output data.

2. The method for frequency enhancement of a cold atom gravimeter based on a long short-term memory network-exponential moving average algorithm as described in claim 1, characterized in that, The smoothing factor for the first exponential moving average smoothing process is less than 5%.

3. The method for frequency enhancement of a cold atom gravimeter based on a long short-term memory network-exponential moving average algorithm as described in claim 1, characterized in that, The continuous input sequence generated by linear interpolation covers the time interval between the original measured points.

4. The method for frequency enhancement of a cold atom gravimeter based on a long short-term memory network-exponential moving average algorithm as described in claim 1, characterized in that, Long Short-Term Memory (LSTM) networks are used for learning and validation by dividing the training set and the test set in a 9:1 ratio.

5. The method for frequency enhancement of a cold atom gravimeter based on a long short-term memory network-exponential moving average algorithm according to claim 1, characterized in that, The predicted value is inserted between adjacent data in the noise-reduced data, thereby doubling the original frequency.

6. The method for frequency enhancement of a cold atom gravimeter based on a long short-term memory network-exponential moving average algorithm according to claim 1, characterized in that, The smoothing factor for the second exponential moving average smoothing process is greater than 50%.

7. A frequency enhancement device for a cold atom gravimeter based on a long short-term memory network-exponential moving average algorithm, characterized in that, include: A module that acquires the raw gravitational acceleration data output by the cold atom gravimeter and performs the first exponential moving average smoothing process to obtain noise-reduced data. A module that performs linear interpolation on the denoised data to generate a continuous input sequence for training and prediction of the Long Short-Term Memory Network; The module that inputs the continuous input sequence into the long short-term memory network, learns the data features, and outputs the predicted value of the gravitational acceleration at the next moment; A module that inserts the predicted value between adjacent data of the noise reduction data to generate a frequency boost sequence composed of the measured data and the predicted data; A module that performs a second exponential moving average smoothing process on the frequency-enhanced sequence to obtain the final high-frequency gravitational acceleration output data.

8. A computer storage medium for storing computer programs, characterized in that, When the computer program is read by the computer, the computer executes the method of claim 1.

9. A computer, comprising a processor and a storage medium, characterized in that, When the processor reads the computer program stored in the storage medium, the computer executes the method of claim 1.

10. A computer program product, as a computer program, is characterized by: When the computer program is executed, it implements the method of claim 1.

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