Clock error prediction method and device, computer device and readable storage medium

Abstract

The application relates to a clock difference prediction method and device, computer equipment and a readable storage medium, comprising: obtaining a to-be-processed clock difference sequence; performing data preprocessing on the to-be-processed clock difference sequence to obtain a standardized residual error sequence; processing the standardized residual error sequence by using a probability-weighted fuzzy time sequence model to obtain a probability-weighted fuzzy time rule set; performing recursive prediction in combination with the fuzzy time rule set to obtain a prediction value set matched with the fuzzy time rule; performing defuzzification processing on the prediction value set to obtain a prediction residual error; performing inverse standardization processing on the prediction residual error and combining the prediction residual error with a trend item fitted and extracted in the data preprocessing process to obtain a target clock difference prediction result. The application eliminates data noise and magnitude difference through data preprocessing, fully captures sequence time sequence characteristics by using a probability-weighted fuzzy time sequence, can effectively improve clock difference prediction accuracy, and provides a reliable clock difference prediction solution for high-precision real-time positioning of a satellite navigation system.

Description

Technical Field

[0001] This application relates to the field of satellite navigation technology, and in particular to a clock error prediction method, apparatus, computer equipment, and readable storage medium. Background Technology

[0002] As a crucial spatiotemporal infrastructure, the Global Navigation Satellite System (GNSS) provides global users with all-weather, high-precision positioning, navigation, and timing (PNT) services. Satellite clock bias is a core parameter affecting the positioning and timing accuracy of a navigation system. It characterizes the deviation between the satellite clock and the system's standard time reference, primarily caused by factors such as atomic clock aging, frequency drift, and environmental disturbances.

[0003] Existing clock error prediction models are mainly divided into two categories. One category is traditional statistical and physical models (such as multinomial models, grey models, Kalman filter models, etc.). These models are difficult to fully capture the complex nonlinear and nonstationary characteristics of clock error sequences, resulting in a bottleneck in prediction performance. The other category is artificial intelligence models (such as LSTM, GRU and other deep learning models). Although they have advantages in nonlinear fitting, they have problems such as hyperparameter sensitivity, strong data dependence, high computational cost and low interpretability, posing potential risks in the application of satellite navigation systems with high reliability requirements.

[0004] Fuzzy Time Series (FTS) methods effectively address the uncertainty and fuzziness of time series data, requiring relatively little data and offering good mathematical interpretability. However, traditional FTS models tend to produce forecasts that exceed the predefined universe of discourse when dealing with non-stationary clock series, leading to decreased forecast accuracy. Therefore, there is an urgent need for a short-term forecasting method that balances accuracy, efficiency, and interpretability while adapting to the non-stationary characteristics of clock series. Summary of the Invention

[0005] Therefore, it is necessary to provide a clock error prediction method, device, computer equipment, and readable storage medium to address the technical problems of insufficient nonlinear modeling capability of traditional models, poor interpretability of deep learning models, and difficulty of traditional fuzzy time series models in adapting to non-stationary sequences.

[0006] In a first aspect, this application provides a clock difference prediction method, the method comprising:

[0007] Obtain the clock difference sequence to be processed;

[0008] The clock difference sequence to be processed is preprocessed to obtain a standardized residual sequence;

[0009] The standardized residual sequence is processed using a probability-weighted fuzzy time series model to obtain a probability-weighted set of fuzzy time rules;

[0010] By combining the aforementioned set of fuzzy time rules for recursive prediction, a set of predicted values ​​matching the fuzzy time rules is obtained;

[0011] The predicted value set is defuzzified to obtain the prediction residual;

[0012] The predicted residuals are inversely standardized and then merged with the trend term extracted during data preprocessing to obtain the target clock error prediction result.

[0013] In one embodiment, the step of preprocessing the clock difference sequence to obtain a standardized residual sequence includes:

[0014] The median absolute deviation method was used to remove outliers from the clock error sequence to be processed.

[0015] The trend term of the clock error sequence to be processed is extracted by polynomial fitting, and the difference between the clock error sequence to be processed and the trend term is calculated to obtain the reference residual sequence.

[0016] The reference residual sequence is standardized using the Z-SCORE standardization method to obtain the standardized residual sequence.

[0017] In one embodiment, the step of processing the standardized residual sequence using a probability-weighted fuzzy time series model to obtain a probability-weighted set of fuzzy time rules includes:

[0018] The training domain of the residual sequence is determined, and the training domain is divided into multiple overlapping sub-intervals, wherein each sub-interval is associated with a corresponding fuzzy set and membership function;

[0019] The standardized residual sequence is converted into a fuzzy time series through the membership function, and a fuzzy logic relation group of a preset order is generated based on the fuzzy time series;

[0020] Calculate the prior probability and conditional probability of each fuzzy rule in the fuzzy logic relation group to obtain the probability-weighted fuzzy time rule set.

[0021] In one embodiment, the step of performing recursive prediction based on the set of fuzzy time rules to obtain a set of predicted values ​​matching the fuzzy time rules includes:

[0022] Determining the clock difference sequence to be predicted based on a sliding window;

[0023] The clock difference sequence to be predicted is converted into a fuzzy time series based on the current membership function;

[0024] The predicted value is obtained by matching and predicting based on the fuzzy time series and the fuzzy time rule set.

[0025] Based on the sliding window, recursive prediction is performed to obtain a set of predicted values ​​that match the fuzzy time rule.

[0026] In one embodiment, the method further includes:

[0027] During the prediction process, it is monitored whether the fuzzy set to which the predicted value belongs is located at the edge of the universe of discourse for a consecutive preset number of times;

[0028] If the fuzzy set to which the predicted value belongs is at the edge of the universe of discourse for a preset number of consecutive times, the distribution parameters of the fuzzy sets corresponding to each sub-interval of the training universe of discourse are dynamically adjusted based on the exponential decay strategy.

[0029] The expected output of each fuzzy set is recalculated based on the adjusted fuzzy set, and the predicted value is obtained again.

[0030] In one embodiment, the edges of the domain are the leftmost or rightmost two fuzzy sets of the training domain; the preset number of iterations is greater than or equal to 2.

[0031] If the fuzzy set to which the predicted value belongs is located at the edge of the universe of discourse for a predetermined number of consecutive times, the distribution parameters of the fuzzy sets corresponding to each sub-interval of the training universe of discourse are dynamically adjusted based on an exponential decay strategy, including:

[0032] If the fuzzy set to which the predicted value belongs is located on the left edge of the training domain for a preset number of consecutive times, adjust the displacement factor and width factor to shift the entire fuzzy set to the left.

[0033] If the fuzzy set to which the predicted value belongs is located on the right edge of the training domain for a preset number of consecutive times, adjust the displacement factor and width factor to shift the entire fuzzy set to the right.

[0034] In one embodiment, the membership function is a trigonometric membership function;

[0035] The static expression of the membership function is:

[0036]

[0037] The dynamic expression of the membership function is:

[0038]

[0039]

[0040] in, Denotes the left endpoint of the fuzzy set. Represents the center point of the fuzzy set. Denotes the right endpoint of the fuzzy set. Represents the displacement factor. This represents the width factor.

[0041] Secondly, this application also provides a clock difference prediction device, the device comprising:

[0042] The acquisition module is used to acquire the clock difference sequence to be processed;

[0043] The preprocessing module is used to preprocess the clock difference sequence to be processed to obtain a standardized residual sequence.

[0044] The training module is used to process the standardized residual sequence using a probability-weighted fuzzy time series model to obtain a probability-weighted set of fuzzy time rules.

[0045] The prediction module is used to perform recursive prediction by combining the set of fuzzy time rules to obtain a set of predicted values ​​that match the fuzzy time rules.

[0046] The post-processing module is used to defuzzify the predicted value set to obtain the prediction residual; to perform inverse standardization on the prediction residual and merge it with the trend term extracted during data preprocessing to obtain the target clock error prediction result.

[0047] Thirdly, this application also provides a computer device. The computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of the clock prediction method described in the first aspect.

[0048] Fourthly, this application also provides a computer-readable storage medium. The computer-readable storage medium stores a computer program thereon, which, when executed by a processor, implements the steps of the clock prediction method described in the first aspect.

[0049] The aforementioned clock error prediction method, apparatus, computer equipment, and readable storage medium include: acquiring a clock error sequence to be processed; performing data preprocessing on the clock error sequence to obtain a standardized residual sequence; processing the standardized residual sequence using a probability-weighted fuzzy time series model to obtain a probability-weighted fuzzy time rule set; performing recursive prediction using the fuzzy time rule set to obtain a set of predicted values ​​matching the fuzzy time rules; defuzzifying the set of predicted values ​​to obtain prediction residuals; performing inverse standardization on the prediction residuals and merging them with the trend term extracted during data preprocessing to obtain the target clock error prediction result. This application eliminates data noise and magnitude differences through data preprocessing and fully captures the temporal characteristics of the sequence using a probability-weighted fuzzy time series model, which can effectively improve the accuracy of clock error prediction and provide a reliable clock error prediction solution for high-precision real-time positioning of satellite navigation systems. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the steps involved in FTS training in one embodiment;

[0051] Figure 2 This is a diagram illustrating the application environment of the clock error prediction method in one embodiment;

[0052] Figure 3 This is a flowchart illustrating a clock error prediction method in one embodiment;

[0053] Figure 4 This is a flowchart illustrating the steps of a clock error prediction method in one embodiment;

[0054] Figure 5 This is a flowchart illustrating the steps of the clock error prediction method in another embodiment;

[0055] Figure 6 This is a schematic diagram illustrating the effect of using multiple clock error prediction models to perform short-term clock error prediction for the C20 satellite in one embodiment.

[0056] Figure 7 This is a schematic diagram illustrating the effect of using multiple clock error prediction models to perform short-term clock error prediction for the C33 satellite in one embodiment.

[0057] Figure 8 This is a schematic diagram illustrating the effect of using multiple clock error prediction models to perform short-term clock error prediction for the C38 satellite in one embodiment.

[0058] Figure 9 This is a schematic diagram illustrating the effect of using multiple clock error prediction models to perform short-term clock error prediction for the C42 satellite in one embodiment.

[0059] Figure 10 This is a schematic diagram of the 6-hour forecast error results available from satellites for BDS-3 in one embodiment;

[0060] Figure 11 This is a schematic diagram illustrating the average error RMSE of multiple forecasting methods used in different atomic clock types in one embodiment;

[0061] Figure 12 This is a schematic diagram illustrating the average error RE of various prediction methods used in different atomic clock types in one embodiment.

[0062] Figure 13 This is a structural block diagram of a clock error prediction device in one embodiment;

[0063] Figure 14 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0064] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0065] Satellite atomic clocks are affected by their own aging and frequency drift, as well as various external environmental factors such as the gravity of celestial bodies, solar radiation, and relativistic effects, resulting in inherent fuzziness and uncertainty in clock bias sequences. Among related technologies, fuzzy time series (FTS) can effectively address the challenges of uncertainty and fuzziness in time series. Compared to deep learning methods, FTS requires less data, can extract effective fuzzy rules from limited historical data, and its probability-based prediction method is more mathematically interpretable.

[0066] Since the introduction of the FTS prediction model, the main differences between models lie in the choice of membership function, the method of fuzzy set partitioning, and the order. This includes aspects such as defuzzification methods and time-varying and non-stationary characteristics. To facilitate understanding of the clock error prediction method provided in this embodiment, the following describes the steps for obtaining fuzzy time series using the FTS prediction model.

[0067] like Figure 1 As shown, the original time series Convert to fuzzy time series The steps include:

[0068] Step 1, Determine the universe of discourse. Given a time series... In this case, the training domain can be defined. The sample space serves as the training data, where... and Can be set to , This is to appropriately expand the training data.

[0069] Step 2, divide the interval. Divide the training domain... Divided into For each overlapping sub-interval, create a corresponding fuzzy set. Define a membership function. Membership function Used to describe which data point belongs to a fuzzy set The degree of.

[0070] Step 3, blurring. The time series... Converted into a fuzzy time series using membership functions Fuzzy time series Each data point It is Dimensional tuples, containing Relative to each fuzzy set The membership value, i.e. .in, express Compared to fuzzy sets The membership degree value.

[0071] Step 4: Establish fuzzy logic relationships. This step can also be called establishing fuzzy logic rules. Specifically, the FTS prediction model is represented by a set of fuzzy logic relationships (i.e., rules) to describe the correlation of fuzzy sets in the time dimension. Each fuzzy logic relationship has... Similar in form. Among them, the left side... This is called the antecedent or left-hand side (LHS) of a fuzzy logic relation. This is called the consequent or right-hand side (RHS) of a fuzzy logic relation.

[0072] In rule-based fuzzy time series theory, this rule can be understood as "if at time..." The observed data points belong to a fuzzy set. And at all times The observed data points belong to a fuzzy set. ,So It may belong to a fuzzy set. "A group of fuzzy logic relations with the same LHS is formed, which can be understood as a fuzzy logic relation group when time..." arrive When the state pattern (antecedent) is identified, time A probabilistic description of the possible states (possible successors).

[0073] To address the shortcomings of traditional models in modeling complex features, and the problems of low interpretability, strong data dependence, and high computational cost of deep learning models, this embodiment provides a short-term difference forecasting method for dynamic non-stationary fuzzy time series, which can balance efficiency, accuracy, and interpretability.

[0074] The clock difference prediction method provided in this application can be applied to, for example... Figure 2 In the application environment shown, terminal 102 communicates with server 104 via a network. Server 104 obtains satellite clock bias data provided by the IGS data center, performs short-term forecasts using the method described in this application, and then feeds back the forecast results to terminal 102 (such as navigation equipment, surveying equipment, etc.). Terminal 102 can be various personal computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. IoT devices can be smart navigation terminals, surveying equipment, etc. Server 104 can be implemented using a standalone server or a server cluster consisting of multiple servers.

[0075] In one embodiment, reference Figure 3 A clock difference prediction method is provided, which can be applied to... Figure 2 Taking server 104 as an example, the following steps are included:

[0076] Step 301: Obtain the clock difference sequence to be processed.

[0077] In this embodiment, the clock difference sequence to be processed refers to the basic clock difference data used for probability-weighted fuzzy time series modeling and clock difference prediction within a preset period. The preset period can be a prediction period within a short timeframe such as 6 hours, 8 hours, 10 hours, or 12 hours. It should be noted that the prediction period of the clock difference prediction method can be configured according to the needs of the actual application scenario. Preferably, the clock difference prediction method provided in this embodiment is preferably used for short-term clock difference prediction to maximize the accuracy, reliability, and efficiency of short-term clock difference prediction while saving costs.

[0078] Specifically, the clock bias sequence to be processed can be BDS-3 satellite clock bias data provided by the IGS data center, including ephemeris files and clock bias files. It should be noted that the actual source and acquisition method of the clock bias sequence to be processed in this embodiment can be configured according to the needs of the actual application scenario. The acquisition method of the clock bias sequence to be processed can be adaptively adjusted according to the differences in the types of equipment used in the clock bias prediction method.

[0079] Step 302: Perform data preprocessing on the clock difference sequence to be processed to obtain a standardized residual sequence.

[0080] In this embodiment, data preprocessing includes several steps such as gross error removal, missing value imputation, trend term filtering, residual sequence calculation, and standardization. The standardized residual sequence refers to the difference between the clock error sequence to be processed and the trend term after standardization.

[0081] In one embodiment, such as Figure 4 As shown, step 302 includes the following steps:

[0082] First, the Median Absolute Deviation (MAD) method is used to remove outliers from the clock error sequence. Specifically, the outlier removal step involves identifying a data point as outlier and removing it if the absolute deviation from the median is greater than three times the MAD. Missing epoch data can be filled in using interpolation. For example, missing epochs can be filled in using cubic spline interpolation.

[0083] Second, a trend term is extracted from the clock error sequence to be processed using polynomial fitting. The difference between the clock error sequence to be processed and the trend term is calculated to obtain a reference residual sequence. It should be noted that the trend term extraction method in this embodiment can adopt a general trend term extraction method. An appropriate fitting extraction method can be selected according to the needs of the actual application scenario.

[0084] Third, the Z-SCORE standardization method is used to standardize the reference residual sequence to obtain a standardized residual sequence. Specifically, since the clock error sequence has a relatively small numerical magnitude, standardizing the reference residual sequence can effectively avoid numerical calculation problems during the forecasting process. In practical applications, other standardization methods that can avoid numerical calculation problems during the forecasting process can also be selected according to the needs of the specific application scenario.

[0085] Step 303: The standardized residual sequence is processed using a probability-weighted fuzzy time series model to obtain a probability-weighted set of fuzzy time rules.

[0086] In this embodiment, Probabilistic Weighted Fuzzy Time Series (PWFTS) effectively addresses the information loss caused by traditional defuzzification methods that only consider the rules corresponding to the fuzzy sets with the highest membership degrees. This embodiment processes the standardized residual sequence using a PWFTS model. By calculating the prior and posterior empirical probabilities of the antecedent and consequent in the fuzzy logic relation group, weights are assigned to all fuzzy rules with membership degrees greater than zero, comprehensively considering complete fuzzy information. Compared to traditional defuzzification methods, PWFTS not only improves prediction accuracy but also enhances the mathematical interpretability of the model.

[0087] The following section will introduce the weight calculation principle, training, and prediction steps of PWFTS.

[0088] In a given sample space (i.e., the training domain) and fuzzy sets In the case of sample space The sample data in the middle is available Indicates, that is For fuzzy sets Any fuzzy set in can be used Indicates, that is , It is a positive integer. Define the partition function. It is a membership function In the sample space The integral on, that is or its discrete approximation For a first-order PWFTS, fuzzy sets The prior probability can be viewed as the sum of the membership degrees of all samples. Divide by all fuzzy sets partitioning function The sum, the formula is as follows:

[0089]

[0090] This formula can be visualized as: prior probability Uniformly distributed throughout the fuzzy set The membership function shape of the point It is an area of ​​this shape. The "slice", and The total area is .

[0091] The fuzzy logical relation groups generated in PWFTS are weighted on the LHS and RHS to measure their fuzzy empirical probabilities. Each probability-weighted fuzzy temporal pattern (PWFTP) has the following form:

[0092]

[0093] in For fuzzy sets Prior probabilities independent of time, i.e. Each weight In time The fuzzy set was identified as Under these conditions, time Fuzzy sets appear The conditional probability, i.e. Furthermore, on the left... At that time, the right piece The normalized values ​​of the FTP membership degree and the sum of the values ​​make it possible for each LHS to... have The specific calculation formula is as follows:

[0094]

[0095] The PWFTP obtained through the above calculation formula represents the temporal dynamics of the raw data, i.e. All possibilities.

[0096] Point prediction is performed using an expected value weighted method, first calculating the expected value of each fuzzy logic rule. ,in Each fuzzy set The midpoint. Each rule's... Expected value It is constant and can be calculated using the following formula:

[0097]

[0098] Final predicted value yes The sum of probability-weighted expected values ​​is given by the following formula:

[0099]

[0100] The above theory is derived to higher-order PWFTS, for The model needs to use PWFTS of order 1. Predicting based on data. Once the values ​​are blurred... If a given set contains multiple fuzzy sets (where the membership degree is greater than zero), then all possible left-hand fuzzy relations (LHS) require Cartesian product calculation. In a PWFTS of order 1, all possible fuzzy relations are: ,in, This represents the Cartesian operator.

[0101] In higher-order PWFTS, Will be replaced with At this time, superscript Represented as all possible antecedent rules, subscript Let denot be a certain antecedent rule, where the prior probability weights represent the weights of all possible antecedent rules. In the table, rules The weights. For a given set of weights... A sample of data The formula for calculating its membership degree under a certain fuzzy logic rule is:

[0102]

[0103] For the partition function Therefore, the formula for calculating the prior probability is:

[0104]

[0105] The conditional probability formula can be rewritten as:

[0106]

[0107] in, Indicates a certain antecedent rule (e.g.) The final point prediction formula will be in the following form:

[0108]

[0109] Higher-order FTS models can identify more complex changes in time series, but excessively high orders can lead to rule redundancy, increasing computational complexity and potentially causing difficulties in rule matching, thus reducing prediction accuracy. In this embodiment, a third-order PWFTS is preferably used for clock bias prediction. It should be noted that the order of the PWFTS model used in this embodiment can be determined according to the needs of the actual application scenario. Using a third-order PWFTS for clock bias prediction can improve prediction accuracy while avoiding rule redundancy and increased computational complexity.

[0110] In one embodiment, reference Figure 4 Step 303 includes the following steps:

[0111] First, determine the training domain of the residual sequence and divide the training domain into multiple overlapping sub-intervals, where each sub-interval is associated with a corresponding fuzzy set and membership function.

[0112] Second, the standardized residual sequence is converted into a fuzzy time series through membership functions, and a fuzzy logic relation group of a preset order is generated based on the fuzzy time series.

[0113] Third, calculate the prior probability and conditional probability of each fuzzy rule in the fuzzy logic relation group to obtain the probability-weighted fuzzy time rule set.

[0114] In this embodiment, after obtaining the standardized residual sequence, the training universe of PWFTS is determined based on the width of the residual sequence. Fuzzy C-means clustering (FCM) is then used to divide the training universe into multiple overlapping sub-intervals. For example... Figure 1As shown, the number of overlapping sub-intervals can be 8, corresponding to 8 fuzzy sets. Each overlapping subinterval, i.e., each fuzzy set, uses a trigonometric function as its membership function. Specifically, the static expression of the trigonometric membership function is:

[0115]

[0116] Wherein, the left endpoint of the fuzzy set Center point and right endpoint Determined by the FCM clustering results, it is used to quantify the degree to which a data point belongs to the fuzzy set.

[0117] In this embodiment, the construction of a third-order probability-weighted fuzzy logic relation is used as an example. Each data point in the standardized residual sequence can be input into a triangular membership function to calculate its membership degree value to each fuzzy set, thus obtaining a fuzzy time series (each data point is a multi-dimensional membership vector). For example, the membership degree value to 8 fuzzy sets is calculated to obtain a fuzzy time series, where each data point is an 8-dimensional membership vector.

[0118] Based on fuzzy time series, high-order fuzzy logical relation groups are generated. For example, a logical relation group is constructed from the fuzzy set of the previous three time steps to the fuzzy set of the next time step. , .

[0119] Based on the aforementioned membership degree calculation formula, prior probability calculation formula, and conditional probability calculation formula, the prior probability and conditional probability of each fuzzy rule in the fuzzy logic relation group are calculated respectively, forming a probability-weighted fuzzy logic relation set, that is, a probability-weighted fuzzy time rule set. Each relation contains prior probability and conditional probability weights.

[0120] Specifically, the formula for calculating the prior probability is:

[0121]

[0122] The formula for calculating conditional probability is:

[0123]

[0124] in, This indicates a certain antecedent rule.

[0125] Step 304: Perform recursive prediction by combining the set of fuzzy time rules to obtain a set of predicted values ​​that match the fuzzy time rules.

[0126] In this embodiment, a sliding window of preset length is used to recursively predict the target clock difference sequence to obtain a set of predicted values, i.e., a predicted fuzzy sequence.

[0127] In practical application scenarios, step 304 includes the following steps:

[0128] The clock difference sequence to be predicted is determined based on a sliding window.

[0129] The clock difference sequence to be predicted is converted into a fuzzy time series based on the current membership function.

[0130] The predicted value is obtained by matching and predicting based on the fuzzy time series and the set of fuzzy time rules.

[0131] Recursive prediction is achieved using a sliding window to obtain a set of predicted values ​​that match the fuzzy temporal rules.

[0132] In this embodiment, the clock error sequence to be predicted is first determined based on the width of the sliding window and the standardized residual sequence. The length of the sliding window can be set according to the needs of the actual application scenario. In a specific embodiment, the length of the sliding window can be set to be greater than or equal to 3.

[0133] For example, for the clock difference sequence to be predicted It can be converted into a fuzzy time series using the membership function of the current state. Then, match all antecedents in the fuzzy time rule set. Fuzzy time rules. All possible values ​​and weights are given by the right-hand side of each matching fuzzy time rule. That is, matching and prediction are performed based on the fuzzy time series and the set of fuzzy time rules to obtain the predicted value. The input window is updated by sliding the window. By repeatedly performing rule matching and matching prediction processing, a set of predicted values ​​that match the fuzzy time rules can be obtained.

[0134] Step 305: Defuzzify the predicted value set to obtain the prediction residual.

[0135] In this embodiment, reference Figure 4 After obtaining the set of predicted values, i.e., the fuzzy set prediction sequence, defuzzification of the predicted value set yields the prediction residual sequence. Further data post-processing can then produce accurate clock error prediction results.

[0136] Step 306: Perform inverse standardization on the prediction residuals and merge them with the trend term extracted during data preprocessing to obtain the target clock error prediction result.

[0137] In this embodiment, data post-processing includes inverse standardization and trend term merging. By inverse standardizing the predicted residuals and adding the fitted trend, the actual predicted value of the clock error, i.e. the target clock error prediction result, can be obtained.

[0138] Based on the above steps, this embodiment provides a clock error prediction method. Compared with traditional defuzzification methods, PWFTS not only improves prediction accuracy but also enhances the mathematical interpretability of the model.

[0139] In practical applications, clock error-fitted residual sequences not only exhibit heteroscedasticity but are also non-stationary processes, with their statistical mean and variance changing over time. In actual predictions, static FTS models may fail to accurately reflect current sequence changes due to the trend term fitted based on historical data, potentially leading to true values ​​exceeding the predefined domain of the probability-weighted fuzzy time series. To address this, this embodiment also provides a dynamic adjustment strategy that continuously monitors forecast results and dynamically adjusts the fuzzy set distribution based on an exponential decay strategy to achieve higher forecast accuracy.

[0140] While retaining the original training framework of PWFTS, this embodiment proposes an adaptive non-stationary fuzzy set adjustment mechanism based on boundary monitoring to address the issue that actual values ​​in clock error forecasts may exceed the universe of discourse set during the training phase. The core of this mechanism is to dynamically adjust the distribution of non-stationary fuzzy sets by monitoring whether the fuzzy set to which the forecast value belongs remains at the edge of the universe of discourse.

[0141] In one embodiment, reference Figure 5 The clock error prediction method also includes the following steps:

[0142] First, during the prediction process, it is monitored whether the fuzzy set to which the predicted value belongs is located at the edge of the universe of discourse for a predetermined number of consecutive times. The edge of the universe of discourse can refer to the two leftmost or two rightmost fuzzy set regions in the training universe of discourse. It should be noted that the edge of the universe of discourse can be defined according to the needs of the actual application scenario; for example, the edge of the universe of discourse can also be the leftmost or rightmost fuzzy set region. The predetermined number of times can be set to 2, 3, or other values, and the actual value of the predetermined number of times can be determined according to the needs of the actual application scenario.

[0143] Second, if the fuzzy set to which the predicted value belongs is located at the edge of the universe of discourse for a predetermined number of consecutive times, the distribution parameters of the fuzzy sets corresponding to each sub-interval of the training universe of discourse are dynamically adjusted based on an exponential decay strategy. In this embodiment, the exponential decay strategy is mainly implemented through a shift factor. and width factor To achieve this.

[0144] Third, recalculate the expected output of each fuzzy set based on the adjusted fuzzy set, and re-obtain the predicted value.

[0145] In this embodiment, non-stationary fuzzy sets (NSFS) are used to implement time-varying FTS. By changing the position and width of the membership function or adding noise over time, the model can continuously adapt to the dynamic changes in the sequence. Compared to methods that repeatedly rebuild the entire model, NSFS does not require global reconstruction, resulting in higher computational efficiency and a simpler implementation. This method is particularly suitable for scenarios such as clock error prediction, which require multi-step prediction through sliding windows.

[0146] Non-stationary fuzzy sets can be represented by the following formula:

[0147]

[0148] in, For the domain Nonstationary fuzzy sets on time, which are derived from time Membership functions are composed of the membership functions of variables; non-stationary membership functions. The parameters change over time. If we represent the static membership function... ,in If the function parameter is , then the non-stationary membership function can be expressed as: The static form of the trigonometric membership function used in this embodiment is:

[0149]

[0150] in, Let these represent the left endpoint, center point, and right endpoint, respectively. Based on the theory of non-stationary fuzzy sets, a displacement factor can be introduced. and width factor To dynamically adjust the membership function. For non-stationary triangular membership functions, a perturbation function is set for the static triangular membership function. To achieve its positional shift, its non-stationary membership function (NSMF) can be expressed as: ,in:

[0151]

[0152] in, Denotes the left endpoint of the fuzzy set. Represents the center point of the fuzzy set. Denotes the right endpoint of the fuzzy set. Represents the displacement factor. This represents the width factor.

[0153] In this embodiment, the non-stationary fuzzy set is adaptively adjusted as the data evolves by designing translation and displacement factors. The core objective of this process is to find a suitable set of values ​​or functions for the dynamic parameters of each non-stationary membership function so that the distribution of the fuzzy set adapts to the changing patterns of the data.

[0154] For example, define the two fuzzy sets at the leftmost and rightmost edges of the training domain as the edges of the domain. Assume the predicted values ​​are continuous. If a fuzzy set belongs to the left edge of the universe of discourse, it indicates that the actual observed value may be below the lower bound of the current universe of discourse. This suggests that the trend term extracted by the polynomial fitting is insufficient to describe the current trend of clock error, and the bias of the trend model needs to be compensated by shifting the entire fuzzy set to the left. Similarly, if the predicted value remains within the right edge of the fuzzy set, the entire fuzzy set needs to be shifted to the right.

[0155] In one embodiment, the edges of the universe of discourse are the leftmost or rightmost two fuzzy sets of the training universe of discourse; the preset number of iterations is greater than or equal to 2.

[0156] If the fuzzy set to which the predicted value belongs is located at the edge of the universe of discourse for a predetermined number of consecutive times, the distribution parameters of the fuzzy sets corresponding to each sub-interval of the training universe of discourse are dynamically adjusted based on an exponential decay strategy, including:

[0157] If the fuzzy set to which the predicted value belongs is located on the left edge of the training domain for a preset number of consecutive times, adjust the shift factor and width factor to shift the entire fuzzy set to the left.

[0158] If the fuzzy set to which the predicted value belongs is located on the right edge of the training domain for a preset number of consecutive times, adjust the shift factor and width factor to shift the entire fuzzy set to the right.

[0159] In this embodiment, after determining the overall fuzzy set translation strategy, it is necessary to design specific calculation methods for the non-stationary fuzzy set parameters (displacement factor and width factor). To ensure that the adjustment effectively adapts to the trend changes in the clock error residual term, while preserving the initial overall fuzzy set distribution obtained from fuzzy C-means clustering (FCM) to the greatest extent possible, this embodiment employs an exponentially decaying displacement factor. The calculation method ensures that the maximum translation is applied to the potentially out-of-bounds edge fuzzy set, and the translation decreases progressively towards the interior of the universe of discourse, as follows:

[0160]

[0161]

[0162] in, , Let be the upper and lower bounds of the domain of discourse. The number of times the predicted value belongs to the edge of the fuzzy set. The adjustment coefficient represents the proportion of the domain boundary shift relative to the total range each time an adjustment is triggered. Under this strategy, the shift is largest for the fuzzy set that may exceed the boundary, and the shift of the fuzzy set thereafter decreases exponentially, compensating for the shortcomings of the trend model while minimizing changes to the overall distribution of the fuzzy sets.

[0163] For width factor This requires ensuring that adjacent fuzzy sets maintain appropriate overlap after translation, avoiding gaps. Assume the desired fuzzy set overlap rate is... Under the exponentially decaying translation strategy, the fuzzy set with the largest decay can be considered as... corresponding Since it is 0, the following derivation can be made:

[0164]

[0165] Right now:

[0166]

[0167] Set the right side of the equation above as... We can obtain:

[0168]

[0169] The corresponding width factor is calculated as follows:

[0170]

[0171]

[0172] Based on the above scheme, it can be guaranteed that the overlap rate between adjacent fuzzy sets is always approximately 1. The prediction method introduces the aforementioned boundary monitoring and dynamic adjustment steps to the original probability-weighted fuzzy time series forecasting. The specific execution flow of the prediction process is as follows: Figure 5 As shown.

[0173] The detection prediction results continue When the two edge fuzzy sets of the next membership fuzzy set are selected, the displacement factor and width factor are calculated according to the above formulas to obtain the updated non-stationary fuzzy set distribution. Then, the expected output of each fuzzy set is recalculated based on the adjusted fuzzy sets. Using the probability-weighted unambiguity resolution formula, this can be re-predicted. The clock error prediction method provided in this embodiment does not change the fuzzy rule base established from the original training data, but only performs local adaptive adjustment of the membership function during the prediction stage. This effectively avoids the contamination of the original probabilistic fuzzy rules by the accumulated error during the recursive prediction process, and enhances the robustness of the model in dynamic changes.

[0174] In a more detailed embodiment, the execution steps of the clock difference prediction method provided in this embodiment are as follows:

[0175] First, the clock error sequence to be processed is preprocessed to obtain a standardized residual sequence, and the training domain of the standardized residual sequence is determined.

[0176] Second, fuzzy C-means clustering (FCM) is used to divide the training domain into multiple overlapping sub-intervals, and a corresponding fuzzy set and triangular membership function are constructed for each sub-interval.

[0177] Third, the standardized residual sequence is converted into a fuzzy time series through the triangular membership function, and a third-order fuzzy logic relation group is generated based on the fuzzy time series.

[0178] Fourth, calculate the prior probability and conditional probability of each fuzzy rule in the fuzzy logic relation set to obtain the probability-weighted fuzzy logic relation set.

[0179] Fifth, based on the sliding window, the target clock difference sequence is recursively predicted. During the prediction process, it is monitored whether the fuzzy set to which the predicted value belongs is continuously at the edge of the universe of discourse for a preset number of times.

[0180] Sixth, if the predicted value belongs to the fuzzy set at the edge of the universe of discourse for a preset number of consecutive times, the displacement factor and width factor of the fuzzy set are dynamically adjusted based on the exponential decay strategy, and then the prediction residual is obtained by probability weighted defuzzification.

[0181] Seventh, the predicted residuals are inversely standardized and merged with the trend terms extracted during data preprocessing to obtain the final clock error prediction result.

[0182] In a more detailed embodiment, to comprehensively evaluate the performance of the dynamic non-stationary fuzzy time series clock bias prediction algorithm provided in this embodiment, the experiment selected ex-post precise clock bias data provided by the IGS data center for experimentation and analysis, covering the period from July 7th to July 11th, 2024, with a clock bias data sampling interval of 5 minutes. Using 12 hours of data as the training set, 6-hour short-term forecasts were performed for all available BDS-3 Middle Earth Orbit (MEO) and Inclined Geosynchronous Orbit (IGSO) satellites during this period. The algorithm's prediction results were compared with two traditional models, Quadratic Programming (QP) and Grey Model (GM), and two deep learning models commonly used in clock bias prediction, Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU). To verify the applicability of the dynamic adjustment strategy, a comparison was made with the basic probability-weighted fuzzy time series forecasting algorithm PWFTS to analyze the predictive performance of the proposed dynamic non-stationary fuzzy time series clock error forecasting method (NSFTS) in this embodiment. All methods performed uniform preprocessing on the original clock error sequence before forecasting: the median absolute deviation method was used for gross error detection and removal, and cubic spline interpolation was used to complete missing epochs. The deep learning model employed differential modeling and a sliding window prediction strategy.

[0183] Root Mean Square Error (RMSE) and Range Error (RE) are used as evaluation metrics to measure prediction accuracy and stability, respectively. The calculation formulas are as follows:

[0184]

[0185]

[0186]

[0187] in, The model represents the first time. The clock difference predicted at each epoch. This indicates that the data provided by IGS after the event, in the precise ephemeris, is from the 1st... The actual clock difference at each epoch. Indicates the total number of predicted epochs. Indicates forecast error, This indicates the maximum forecast error. This represents the minimum forecast error. This represents the root mean square error. Indicates the error range.

[0188] Considering the impact of different orbit types and different types of onboard atomic clocks on forecast performance, atomic clock types can be divided into MEO hydrogen clocks, MEO rubidium clocks, and IGSO hydrogen clocks.

[0189] Figure 6 , Figure 7 , Figure 8 and Figure 9 The images show the RMSE curves of the 6-hour forecast error using data from the 12 hours prior to July 7, 2024, from four representative BDS-3 satellites. The horizontal axis represents the forecast time (in hours), and the vertical axis represents the RMSE error within the corresponding time period.

[0190] like Figures 6-9 As shown, all models exhibit error accumulation over time, with deep learning methods demonstrating superior prediction accuracy compared to traditional methods. The dynamic non-stationary fuzzy time series clock error prediction method proposed in this embodiment demonstrates better prediction accuracy over a 6-hour period, with a more gradual and stable error progression. Specifically: for the C20 satellite, the basic PWFTS method suffers from poor prediction accuracy due to the non-stationarity of the residual sequence leading to an unreasonable initial fuzzy set partitioning. The NSFTS method effectively addresses this issue through a dynamic adjustment mechanism, achieving higher accuracy. For the C33 satellite, its residual sequence does not exceed the initial universe of discourse; therefore, NSFTS does not trigger the adjustment mechanism, degenerating into standard PWFTS, with their error curves largely overlapping. For the C38 and C42 satellites, dynamic adjustment of the fuzzy set is triggered, and the prediction accuracy of NSFTS is slightly higher than that of static PWFTS.

[0191] To more comprehensively evaluate the forecast accuracy and precision of the method in this embodiment, Figure 10 The 6-hour average error RMSE for all available BDS-3 satellites using different models is given.

[0192] like Figure 10 As shown, the method proposed in this embodiment has better forecast accuracy on most satellites. Traditional methods QP and GM have higher errors, while deep learning methods LSTM and GRU have comparable forecast accuracy to the method in this embodiment on a few satellites, but their parameter selection and training time costs are greater. This result verifies the effectiveness and superiority of NSFTS in clock error forecast accuracy. To further quantify and evaluate the algorithm performance, Figure 11 and Figure 12The average errors RMSE and RE of several forecasting methods for different atomic clock types were statistically analyzed. Tables 1 and 2 record the specific values ​​of the evaluation indicators in detail.

[0193] Table 1 shows the RMSE errors for different clock types in the six models.

[0194] Table 1

[0195]

[0196] Table 2 shows the error RE for different clock types in the six models.

[0197] Table 2

[0198]

[0199] like Figure 11 As clearly shown in Table 2, the dynamic non-stationary fuzzy time series forecasting algorithm achieves the highest prediction accuracy across different atomic clock types, with an average forecast error (RMSE) of 0.156 ns. This represents an improvement of 70.2% and 61.7% compared to the QP and GM models, respectively, and 36.5% and 31.8% compared to the LSTM and GRU models, respectively. It also improves upon PWFTS by 11.3%. The algorithm maintains better prediction stability, with an average forecast error range (RE) of 0.382 ns, representing improvements of 55.8% and 36.1% compared to the QP and GM models, respectively, and 27.6% and 23.9% compared to the LSTM and GRU models, respectively. It also surpasses PWFTS by 5.6%. The traditional QP model struggles to capture the complex nonlinear characteristics of clock errors caused by factors such as orbital period and solar radiation, resulting in the largest error. The GM model outperforms QP in short-term forecasts trained with limited data, but its error remains relatively large. Due to the limited training data and the difficulty in achieving global optimization of hyperparameters, the deep learning model's potential in short-term forecasting tasks was not fully realized, resulting in lower accuracy compared to the fuzzy time series method proposed in this paper. To verify the algorithm's robustness over longer time periods, a dataset of precise clock difference products from July 7th to July 11th, 2024, was divided into daily units, and five independent experiments were conducted. The average accuracy was used as the performance evaluation metric. The experimental results are shown in Table 3, which displays the 5-day forecast accuracy of different models.

[0200] Table 3

[0201]

[0202] Table 3 shows that the clock error prediction method provided in this embodiment exhibits the best prediction accuracy in five independent experiments. The dynamic non-stationary prediction method achieves a 5-day average error accuracy of 0.163 ns, representing improvements of 67.5% and 59.5% compared to QP and GM models, 28.8% and 23.1% compared to LSTM and GRU models, and 12.3% compared to PWFTS. In summary, the clock error prediction method provided in this embodiment is a data-driven non-parametric model that does not rely on specific mathematical modeling of the clock error sequence. Instead, it extracts fuzzy logical relationships from historical data and uses a sliding window for recursive prediction. Through a probability weighting mechanism, its prediction process has good mathematical interpretability. The core advantage of this method lies in its adaptive solution to the problem of some satellite clock error residual sequences exceeding the preset universe of discourse through a dynamic non-stationary mechanism, achieving the highest prediction accuracy and optimal error stability under different satellite clock types.

[0203] It should be noted that the satellite clock bias data involved in this application are all from publicly authorized data from IGS, and the collection, use and processing of the data comply with relevant laws, regulations and industry standards.

[0204] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0205] Based on the same inventive concept, this application also provides a clock difference prediction device for implementing the clock difference prediction method described above. The solution provided by this device is similar to the solution described in the above method; therefore, the specific limitations in one or more clock difference prediction device embodiments provided below can be found in the limitations of the clock difference prediction method described above, and will not be repeated here.

[0206] In one embodiment, such as Figure 13 As shown, a clock error prediction device 1300 is provided, including: an acquisition module 1310, a preprocessing module 1320, a training module 1330, a prediction module 1340, and a post-processing module 1350, wherein:

[0207] The acquisition module 1310 is used to acquire the clock difference sequence to be processed.

[0208] The preprocessing module 1320 is used to preprocess the clock difference sequence to be processed to obtain a standardized residual sequence.

[0209] Training module 1330 is used to process standardized residual sequences using a probability-weighted fuzzy time series model to obtain a probability-weighted set of fuzzy time rules.

[0210] The prediction module 1340 is used to perform recursive prediction by combining the set of fuzzy time rules to obtain a set of predicted values ​​that match the fuzzy time rules.

[0211] The post-processing module 1350 is used to defuzzify the predicted value set to obtain the prediction residual; to perform inverse standardization on the prediction residual and to merge it with the trend term extracted during the data preprocessing to obtain the target clock error prediction result.

[0212] In one embodiment, the preprocessing module 1320 is further configured to remove gross errors from the clock error sequence to be processed using the median absolute deviation method; extract the trend term of the clock error sequence to be processed using polynomial fitting; calculate the difference between the clock error sequence to be processed and the trend term to obtain a reference residual sequence; and standardize the reference residual sequence using the Z-SCORE standardization method to obtain the standardized residual sequence.

[0213] In one embodiment, the training module 1330 is further configured to determine the training domain of the residual sequence, divide the training domain into multiple overlapping sub-intervals, wherein each sub-interval is associated with a corresponding fuzzy set and membership function; convert the standardized residual sequence into a fuzzy time series through the membership function, generate a fuzzy logic relation group of a preset order based on the fuzzy time series; calculate the prior probability and conditional probability of each fuzzy rule in the fuzzy logic relation group to obtain the probability-weighted fuzzy time rule set.

[0214] In one embodiment, the prediction module 1340 is further configured to determine the clock difference sequence to be predicted based on a sliding window; convert the clock difference sequence to be predicted into a fuzzy time series according to the current membership function; perform matching prediction based on the fuzzy time series and the fuzzy time rule set to obtain a predicted value; and perform recursive prediction based on the sliding window to obtain a set of predicted values ​​that match the fuzzy time rules.

[0215] In one embodiment, the prediction module 1340 is further configured to monitor, during the prediction process, whether the fuzzy set to which the predicted value belongs is at the edge of the universe of discourse for a consecutive preset number of times; if the fuzzy set to which the predicted value belongs is at the edge of the universe of discourse for a consecutive preset number of times, dynamically adjust the distribution parameters of the fuzzy sets corresponding to each sub-interval of the training universe of discourse based on the exponential decay strategy; recalculate the expected output of each fuzzy set according to the adjusted fuzzy set, and re-acquire the predicted value.

[0216] In one embodiment, the prediction module 1340 is further configured to adjust the displacement factor and the width factor to shift the entire fuzzy set to the left if the fuzzy set to which the predicted value belongs is located on the left edge of the training domain for a consecutive preset number of times; and to adjust the displacement factor and the width factor to shift the entire fuzzy set to the right if the fuzzy set to which the predicted value belongs is located on the right edge of the training domain for a consecutive preset number of times.

[0217] Each module in the aforementioned clock prediction device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0218] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 14 As shown, the computer device includes a processor, memory, input / output interfaces, a communication interface, a display unit, and an input device. The processor, memory, and input / output interfaces are connected via a system bus, and the communication interface, display unit, and input device are also connected to the system bus via the input / output interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The input / output interfaces are used for exchanging information between the processor and external devices. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, mobile cellular networks, NFC (Near Field Communication), or other technologies. When the computer program is executed by the processor, it implements a clock prediction method. The display unit is used to form a visually visible image and can be a display screen, a projection device, or a virtual reality imaging device. The display screen can be an LCD screen or an e-ink screen. The input device of the computer device can be a touch layer covering the display screen, or buttons, trackballs, or touchpads set on the casing of the computer device, or external keyboards, touchpads, or mice, etc.

[0219] Those skilled in the art will understand that Figure 14 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0220] In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the following steps:

[0221] Obtain the clock difference sequence to be processed;

[0222] The clock error sequence to be processed is preprocessed to obtain a standardized residual sequence;

[0223] A probability-weighted fuzzy time series model is used to process the standardized residual series to obtain a probability-weighted set of fuzzy time rules.

[0224] By combining the set of fuzzy time rules for recursive prediction, a set of predicted values ​​matching the fuzzy time rules is obtained;

[0225] The prediction residuals are obtained by defuzzifying the predicted value set.

[0226] The prediction residuals are inversely standardized and then merged with the trend term extracted during data preprocessing to obtain the target clock error prediction results.

[0227] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program performing the following steps when executed by a processor:

[0228] Obtain the clock difference sequence to be processed;

[0229] The clock error sequence to be processed is preprocessed to obtain a standardized residual sequence;

[0230] A probability-weighted fuzzy time series model is used to process the standardized residual series to obtain a probability-weighted set of fuzzy time rules.

[0231] By combining the set of fuzzy time rules for recursive prediction, a set of predicted values ​​matching the fuzzy time rules is obtained;

[0232] The prediction residuals are obtained by defuzzifying the predicted value set.

[0233] The prediction residuals are inversely standardized and then merged with the trend term extracted during data preprocessing to obtain the target clock error prediction results.

[0234] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, performs the following steps:

[0235] Obtain the clock difference sequence to be processed;

[0236] The clock error sequence to be processed is preprocessed to obtain a standardized residual sequence;

[0237] A probability-weighted fuzzy time series model is used to process the standardized residual series to obtain a probability-weighted set of fuzzy time rules.

[0238] By combining the set of fuzzy time rules for recursive prediction, a set of predicted values ​​matching the fuzzy time rules is obtained;

[0239] The prediction residuals are obtained by defuzzifying the predicted value set.

[0240] The prediction residuals are inversely standardized and then merged with the trend term extracted during data preprocessing to obtain the target clock error prediction results.

[0241] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0242] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0243] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A clock difference prediction method, characterized in that, The method includes: Obtain the clock difference sequence to be processed; The clock difference sequence to be processed is preprocessed to obtain a standardized residual sequence; The standardized residual sequence is processed using a probability-weighted fuzzy time series model to obtain a probability-weighted set of fuzzy time rules; By combining the aforementioned set of fuzzy time rules for recursive prediction, a set of predicted values ​​matching the fuzzy time rules is obtained; The predicted value set is defuzzified to obtain the prediction residual; The predicted residuals are inversely standardized and then merged with the trend term extracted during data preprocessing to obtain the target clock error prediction result. The standardized residual sequence is processed using a probability-weighted fuzzy time series model to obtain a probability-weighted set of fuzzy time rules, including: The training domain of the residual sequence is determined, and the training domain is divided into multiple overlapping sub-intervals, wherein each sub-interval is associated with a corresponding fuzzy set and membership function; The standardized residual sequence is converted into a fuzzy time series through the membership function, and a fuzzy logic relation group of a preset order is generated based on the fuzzy time series; Calculate the prior probability and conditional probability of each fuzzy rule in the fuzzy logic relation group to obtain the probability-weighted fuzzy time rule set.

2. The method according to claim 1, characterized in that, The step of preprocessing the clock difference sequence to obtain a standardized residual sequence includes: The median absolute deviation method was used to remove outliers from the clock error sequence to be processed. The trend term of the clock error sequence to be processed is extracted by polynomial fitting, and the difference between the clock error sequence to be processed and the trend term is calculated to obtain the reference residual sequence. The reference residual sequence is standardized using the Z-SCORE standardization method to obtain the standardized residual sequence.

3. The method according to claim 1, characterized in that, The recursive prediction based on the set of fuzzy time rules, to obtain a set of predicted values ​​matching the fuzzy time rules, includes: Determining the clock difference sequence to be predicted based on a sliding window; The clock difference sequence to be predicted is converted into a fuzzy time series based on the current membership function; The predicted value is obtained by matching and predicting based on the fuzzy time series and the fuzzy time rule set. Based on the sliding window, recursive prediction is performed to obtain a set of predicted values ​​that match the fuzzy time rule.

4. The method according to claim 3, characterized in that, The method further includes: During the prediction process, it is monitored whether the fuzzy set to which the predicted value belongs is located at the edge of the universe of discourse for a consecutive preset number of times; If the fuzzy set to which the predicted value belongs is at the edge of the universe of discourse for a preset number of consecutive times, the distribution parameters of the fuzzy sets corresponding to each sub-interval of the training universe of discourse are dynamically adjusted based on the exponential decay strategy. The expected output of each fuzzy set is recalculated based on the adjusted fuzzy set, and the predicted value is obtained again.

5. The method according to claim 4, characterized in that, The edges of the universe of discourse are the leftmost or rightmost two fuzzy sets of the training universe of discourse; the preset number of iterations is greater than or equal to 2. If the fuzzy set to which the predicted value belongs is located at the edge of the universe of discourse for a predetermined number of consecutive times, the distribution parameters of the fuzzy sets corresponding to each sub-interval of the training universe of discourse are dynamically adjusted based on an exponential decay strategy, including: If the fuzzy set to which the predicted value belongs is located on the left edge of the training domain for a preset number of consecutive times, adjust the displacement factor and width factor to shift the entire fuzzy set to the left. If the fuzzy set to which the predicted value belongs is located on the right edge of the training domain for a preset number of consecutive times, adjust the displacement factor and width factor to shift the entire fuzzy set to the right.

6. The method according to claim 4, characterized in that, The membership function is a trigonometric membership function; The static expression of the membership function is: The dynamic expression of the membership function is: in, Denotes the left endpoint of the fuzzy set. Represents the center point of the fuzzy set. Denotes the right endpoint of the fuzzy set. Represents the displacement factor. This represents the width factor.

7. A clock difference prediction device, characterized in that, The device includes: The acquisition module is used to acquire the clock difference sequence to be processed; The preprocessing module is used to preprocess the clock difference sequence to be processed to obtain a standardized residual sequence. The training module is used to process the standardized residual sequence using a probability-weighted fuzzy time series model to obtain a probability-weighted set of fuzzy time rules. The prediction module is used to perform recursive prediction by combining the set of fuzzy time rules to obtain a set of predicted values ​​that match the fuzzy time rules. The post-processing module is used to defuzzify the predicted value set to obtain the prediction residual; to perform inverse standardization on the prediction residual and merge it with the trend term extracted during data preprocessing to obtain the target clock error prediction result. The training module is further configured to determine the training domain of the residual sequence and divide the training domain into multiple overlapping sub-intervals, wherein each sub-interval is associated with a corresponding fuzzy set and membership function. The standardized residual sequence is converted into a fuzzy time series through the membership function, and a fuzzy logic relation group of a preset order is generated based on the fuzzy time series; Calculate the prior probability and conditional probability of each fuzzy rule in the fuzzy logic relation group to obtain the probability-weighted fuzzy time rule set.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the clock prediction method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the clock prediction method according to any one of claims 1 to 6.

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