Navigation satellite clock error forecasting method based on inter-satellite measurement and related device

Abstract

The invention belongs to the technical field of navigation satellite clock correction forecasting, and discloses a navigation satellite clock correction forecasting method based on inter-satellite measurement and a related device. The navigation satellite clock error forecasting method comprises the following steps: acquiring a navigation satellite clock error; based on the navigation satellite clock error, establishing a clock error forecast combination model; based on the clock correction prediction combination model, obtaining a navigation satellite clock correction prediction result of a selected time period in the future; wherein in the process of establishing the clock error forecasting combination model, trend term modeling is firstly carried out by using a quadratic polynomial, then periodic term modeling is carried out on residual data by using a Lomb-Scargle spectrum analysis method, and finally, trend term modeling and periodic term modeling results are linearly superposed to obtain the final clock error forecasting combination model. According to the technical scheme disclosed by the invention, satellite clock correction prediction can be supported when the navigation satellite operates autonomously or the ground operation and control service is interrupted, and meanwhile, the clock correction performance of the system in an autonomous operation mode can be improved.

Description

Technical Field

[0001] This invention belongs to the field of navigation satellite clock bias prediction technology, and relates to the intersection of satellite navigation and time and frequency measurement. In particular, it relates to a navigation satellite clock bias prediction method and related device based on inter-satellite measurement. Background Technology

[0002] With the full deployment of the BeiDou-3 Global Navigation Satellite System (BDS-3), the globalization of its positioning, navigation, and timing services has placed higher demands on the accuracy of clock bias modeling and prediction for onboard atomic clocks. To elaborate further, traditional clock bias determination methods based on ground monitoring stations are insufficient to meet the demands of high-precision global services due to the inability to deploy stations globally. Furthermore, while inter-satellite link (ISL) technology can enable clock bias observation of overseas satellites, achieving full-arc tracking, multiple ISL links between satellites may increase measurement errors. Additionally, relying solely on ISLs for autonomous operation can cause constellation drift, severely limiting long-term autonomous operation capabilities. Moreover, while ground-based anchoring can mitigate constellation drift to some extent, it increases dependence on the ground, still failing to achieve truly long-term autonomous operation.

[0003] The next generation of BeiDou satellites is planned to be equipped with higher-precision onboard atomic clocks. Using a high-precision atomic clock from one BeiDou satellite as a reference master clock, other satellites can conduct two-way inter-satellite measurements to determine the satellite clock bias. However, under actual inter-satellite measurement conditions, due to limitations such as geometric visibility and satellite resource allocation, the measurement data between satellites exhibits uneven and discontinuous distribution, resulting in significant non-stationary characteristics in the clock bias information. Specifically, for example, inter-satellite links are constrained by satellite orbital dynamics and visibility, leading to intermittent interruptions in their ISL measurement data. This makes it difficult to fully capture the periodic terms implicit in the clock bias sequence using traditional modeling methods. Furthermore, if interpolation methods are used to complete the data, new errors can easily be introduced when the data loss rate is too high.

[0004] Currently, the clock error models widely used both domestically and internationally have their own limitations, and a new clock error modeling scheme is urgently needed. To be more specific, existing polynomial models fail to take into account periodic terms and noise, causing forecast errors to increase rapidly with the increase of forecast time. Existing traditional grey models and ARIMA models require time series data to be equally spaced, which cannot be well adapted to the modeling and processing of inter-satellite link measured data. The accuracy of existing Kalman filter models depends on information such as the state equation of the atomic clock and the noise model. Existing neural network models require a large number of training samples and have the problem of determining the network structure and optimizing hyperparameters. Summary of the Invention

[0005] The purpose of this invention is to provide a navigation satellite clock bias prediction method and related apparatus based on inter-satellite measurements to solve one or more of the aforementioned technical problems. The technical solution disclosed in this invention can support satellite clock bias prediction during autonomous navigation satellite operation or when ground control services are interrupted, while also improving the clock bias performance of the system in autonomous operation mode.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] In a first aspect, the present invention provides a method for predicting navigation satellite clock bias based on inter-satellite measurements, comprising the following steps:

[0008] Obtain navigation satellite clock bias;

[0009] Based on the clock bias of the navigation satellites, a clock bias prediction combination model is established;

[0010] Based on the clock error prediction combination model, the navigation satellite clock error prediction results for a selected time period in the future are obtained;

[0011] In the process of establishing the clock error prediction combination model, the trend term is first modeled using a quadratic polynomial, then the periodic term is modeled using the Lomb-Scargle spectral analysis method on the residual data, and finally the trend term modeling and periodic term modeling results are linearly superimposed to obtain the final clock error prediction combination model.

[0012] A further improvement to the technical solution of the present invention lies in that, in the clock difference prediction combination model,

[0013] The trend term is modeled as follows:

[0014] Δt(t i )=a0+a1(t i -t0)+a2(t i -t0) 2 +ε(t i );

[0015] In the formula, Δt i t is the satellite clock bias at epoch i; t0 is the reference time for the star clock parameters; t i ε represents the epoch time; a0, a1, and a2 represent the phase, frequency, and frequency drift rate at the reference time, respectively; ε is the fitting error.

[0016] A further improvement to the technical solution of this invention lies in that, in the clock difference prediction combination model, the periodic term modeling includes:

[0017] A frequency network is constructed based on the Nyquist-Shannon sampling theorem, and the frequency search range is set to... Among them, T obst represents the total observation duration. s The median of the sampling interval;

[0018] For each frequency point f, the phase deviation caused by non-equal interval sampling is eliminated by the phase correction function, expressed as:

[0019]

[0020] In the formula, t i τ is the epoch time; τ(f) is the phase deviation corresponding to each frequency point;

[0021] The power value of the periodogram is calculated using the orthogonal basis projection method, and the expression is:

[0022]

[0023] In the formula, y i The residual is the result of fitting a quadratic polynomial to the clock error; σ 2 For y i The variance;

[0024] Based on the extracted significant periodic components f k Construct a multi-harmonic regression model, the expression of which is:

[0025]

[0026] In the formula,

[0027] X=[sin(2πf1t),cos(2πf1t),…,sin(2πf K t),cos(2πf K t)];

[0028]

[0029] In the formula, f1, f2, ..., f K W represents the weight of the extracted significant periodic components.

[0030] Among them, in the significant periodic component f k During the extraction process, a significance threshold of P is set. th =0.2×max(P(f)) to filter out non-significant frequency components.

[0031] A further improvement to the technical solution of the present invention is that, in the step of obtaining the navigation satellite clock bias,

[0032] The navigation satellite clock bias is the navigation satellite clock bias for a selected historical period before the ground operation and control service was interrupted; or, the navigation satellite clock bias is the calculated value or forecast result of the navigation satellite clock bias for a selected historical period after the ground operation and control service was interrupted.

[0033] A further improvement to the technical solution of the present invention is that, when the navigation satellite clock bias is the calculated value of the navigation satellite clock bias for a selected historical time period after the ground operation and control service is interrupted, the step of obtaining the calculated value of the navigation satellite clock bias includes:

[0034] Based on the selected reference satellite, inter-satellite two-way time comparison measurements are performed to obtain the navigation satellite clock bias solution; among which,

[0035] When performing inter-satellite two-way time comparison measurements, the following are included:

[0036] First, the inter-satellite measurement data is preprocessed to obtain effective paired observation data; the preprocessing includes outlier removal and data pairing.

[0037] Based on effective paired observation data, inter-satellite relative clock bias is calculated to obtain navigation satellite clock bias values.

[0038] A second aspect of the present invention provides a navigation satellite clock bias prediction system based on inter-satellite measurements, comprising:

[0039] The data acquisition module is used to acquire navigation satellite clock bias.

[0040] The model building module is used to establish a clock bias prediction combination model based on the clock bias of the navigation satellites;

[0041] The clock error prediction module is used to obtain navigation satellite clock error prediction results for a selected time period in the future based on the clock error prediction combination model.

[0042] In the process of establishing the clock error prediction combination model, the trend term is first modeled using a quadratic polynomial, then the periodic term is modeled using the Lomb-Scargle spectral analysis method on the residual data, and finally the trend term modeling and periodic term modeling results are linearly superimposed to obtain the final clock error prediction combination model.

[0043] A further improvement to the technical solution of the present invention lies in that, in the clock difference prediction combination model,

[0044] The trend term is modeled as follows:

[0045] Δt(t i )=a0+a1(t i -t0)=a2(t i -t0) 2 +ε(t i );

[0046] In the formula, Δt i t is the satellite clock bias at epoch i; t0 is the reference time for the star clock parameters; t iε represents the epoch time; a0, a1, and a2 represent the phase, frequency, and frequency drift rate at the reference time, respectively; ε is the fitting error.

[0047] A further improvement to the technical solution of this invention lies in that, in the clock difference prediction combination model, the periodic term modeling includes:

[0048] A frequency network is constructed based on the Nyquist-Shannon sampling theorem, and the frequency search range is set to... Among them, T obs t represents the total observation duration. s The median of the sampling interval;

[0049] For each frequency point f, the phase deviation caused by non-equal interval sampling is eliminated by the phase correction function, expressed as:

[0050]

[0051] In the formula, t i τ is the epoch time; τ(f) is the phase deviation corresponding to each frequency point;

[0052] The power value of the periodogram is calculated using the orthogonal basis projection method, and the expression is:

[0053]

[0054] In the formula, y i The residual is the result of fitting a quadratic polynomial to the clock error; σ 2 For y i The variance;

[0055] Based on the extracted significant periodic components f k Construct a multi-harmonic regression model, the expression of which is:

[0056]

[0057] In the formula,

[0058] X=[sin(2πf1t),cos(2πf1t),…,sin(2πf K t),cos(2πf K t)];

[0059]

[0060] In the formula, f1, f2, ..., f K W represents the weight of the extracted significant periodic components.

[0061] Among them, in the significant periodic component f k During the extraction process, a significance threshold of P is set.th =0.2×max(P(f)) to filter out non-significant frequency components.

[0062] In a third aspect, the present invention provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the navigation satellite clock bias prediction method based on inter-satellite measurements as described in any one of the first aspects of the present invention.

[0063] In a fourth aspect, the present invention provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the navigation satellite clock bias prediction method based on inter-satellite measurements as described in any one of the first aspects of the present invention.

[0064] Compared with the prior art, the present invention has the following beneficial effects:

[0065] The method for predicting navigation satellite clock bias based on inter-satellite measurement data provided by this invention can support satellite clock bias prediction during autonomous operation of navigation satellites or when ground control services are interrupted. It is mainly applicable when a ground station of the satellite navigation system malfunctions and cannot continue to provide clock bias prediction services to the navigation system. In this case, the navigation satellite needs to autonomously determine the satellite clock bias using inter-satellite measurement data and perform clock bias modeling and prediction, thereby improving the clock bias performance of the system in autonomous operation mode. Explained, the clock bias prediction combined model used in this invention is a combination model of QP and LS. First, a quadratic polynomial QP is used to model the trend term, then the Lomb-Scargle (LS) spectral analysis method is used to model the periodic term on the residual data, and finally, the two are linearly superimposed to obtain the final combined model. To further explain, existing traditional QP models neglect periodicity and random noise, leading to the accumulation of long-term forecast errors. In view of this problem, the LS method of this invention extracts orbital-related periods (such as 12-hour and 6-hour periods caused by Earth's rotation and revolution) from the residuals, compensating for the QP model's neglect of periodic variations. In summary, this invention significantly suppresses long-term forecast error divergence by adding a periodic term to the model. Existing grey models and ARIMA models require strictly equal-interval data, while inter-satellite link measured data has long periods of interruption or non-uniform sampling. In view of this problem, the LS spectral analysis used in this invention can directly process non-uniformly sampled data without interpolation or resampling, avoiding the introduction of additional errors. Therefore, it effectively avoids the modeling failure problem caused by non-uniform data intervals in traditional models. Existing Kalman filtering requires pre-setting state equations and noise statistical characteristics, making accurate modeling difficult in practice. In view of this problem, the combined QP and LS model of this invention separates trend and periodic terms from the data, eliminating the need to pre-set atomic clock dynamic equations, reducing reliance on prior knowledge, and improving model universality. Existing neural networks require a large number of training samples, have complex network structures, and are prone to getting trapped in local optima. In view of the above problems, the QP model of this invention has few parameters (only 3), and LS spectral analysis is computationally efficient. The combination of the two eliminates the need for iterative training. LS automatically determines the main period through significance testing (such as confidence threshold), avoiding parameter tuning problems such as the number of hidden layer nodes and learning rate in neural networks. In summary, this invention achieves high-precision forecasting with limited data and is suitable for real-time or near-real-time applications. Attached Figure Description

[0066] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0067] Figure 1This is a flowchart illustrating a navigation satellite clock bias prediction method based on inter-satellite measurements, as described in an embodiment of the present invention.

[0068] Figure 2 This is a schematic diagram of the uplink and downlink pseudorange of the C19-C21 satellite combination in an embodiment of the present invention;

[0069] Figure 3 This is a schematic diagram of quadratic polynomial fitting for the C19-C21 satellite combination in an embodiment of the present invention;

[0070] Figure 4 This is a schematic diagram of the LS periodic analysis of the C19-C21 satellite combination in an embodiment of the present invention;

[0071] Figure 5 This is a schematic diagram of 24-hour prediction for the C19-C21 satellite combination in an embodiment of the present invention;

[0072] Figure 6 This is a schematic diagram of a navigation satellite clock error prediction system based on inter-satellite measurements, as described in an embodiment of the present invention. Detailed Implementation

[0073] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention; obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0074] Based on the technical solutions disclosed in the embodiments of this invention, all other embodiments obtained by those skilled in the art without inventive effort are within the scope of protection of this invention. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to these processes, methods, products, or devices.

[0075] Please see Figure 1 This invention provides a navigation satellite clock bias prediction method based on inter-satellite measurements, which can support satellite clock bias prediction when navigation satellites are operating autonomously or when ground control services are interrupted. The 12-hour prediction accuracy is better than 0.5 ns. The method includes the following steps:

[0076] Step 1: Obtain the navigation satellite clock bias;

[0077] Step 2: Based on the navigation satellite clock bias obtained in Step 1, establish a clock bias prediction combination model;

[0078] Step 3: Based on the clock error prediction combination model established in Step 2, obtain the navigation satellite clock error prediction results for a selected time period in the future;

[0079] In the process of establishing the clock error prediction combination model, the trend term is first modeled using a quadratic polynomial, then the periodic term is modeled using the Lomb-Scargle spectral analysis method on the residual data, and finally the trend term modeling and periodic term modeling results are linearly superimposed to obtain the final clock error prediction combination model.

[0080] In a preferred embodiment of the technical solution of the present invention, in step 1, during the process of obtaining the navigation satellite clock bias, the navigation satellite clock bias is the navigation satellite clock bias for a selected time period before the ground operation and control service is interrupted; or, the navigation satellite clock bias is the calculated value or forecast result of the navigation satellite clock bias for a selected time period after the ground operation and control service is interrupted.

[0081] In a specific exemplary technical solution of the present invention, step 1, the specific steps for obtaining the navigation satellite clock bias include:

[0082] Based on the selected reference satellite, inter-satellite two-way time comparison measurements are performed to obtain the navigation satellite clock bias solution; among which,

[0083] Based on a reference satellite, two-way inter-satellite measurements are performed to determine satellite clock bias data. When satellites lose ground communication, they can only achieve time synchronization with the navigation system through autonomous measurements between satellites. A satellite is selected as the reference satellite in the navigation network, or a spacecraft such as a space station is selected as the reference satellite. The onboard atomic clock of the reference satellite has high performance, and its deviation from the system time (clock bias) is relatively stable within a certain time range, so the clock bias of the reference satellite can be considered zero. Then, the navigation satellites that need to perform clock bias update predictions are compared and measured in two directions with the reference satellite to obtain the relative clock bias between the two. This clock bias is the navigation satellite clock bias and is used as training data for satellite clock bias prediction.

[0084] When performing inter-satellite two-way time comparison measurements, the following are included:

[0085] (1) First, preprocess the inter-satellite measurement data;

[0086] Specifically, for example, the ranging files used (ISL observation data) need to be preprocessed, including outlier removal and data pairing, to obtain valid paired observation data; wherein,

[0087] The steps for removing outliers are as follows: Based on the characteristics of the two-way pseudorange data, the interquartile range (IQR) method is selected for outlier removal. Explained, the IQR principle is as follows: After sorting the data in ascending order, the value at the 25th percentile (i.e., the maximum value ≤ 25% of the data) is Q1; the value at the 75th percentile (i.e., the minimum value ≥ 75% of the data) is Q3; the interquartile range (IQR) = Q3 - Q1. Outlier detection boundaries are set: the lower limit is Q1 - k × IQR; the upper limit is Q3 + k × IQR; k is typically taken as 1.5. For a data point, if it exceeds the boundary, it can be considered a gross error and removed. The IQR boundary is dynamically calculated every 2 hours using a sliding window, and gross error detection and removal are performed.

[0088] The data pairing steps are as follows: During bidirectional measurement, the downlink pseudorange and uplink pseudorange measurements are not performed simultaneously; in the BeiDou-3 system, the time difference is less than 3 seconds. Specifically, there is a time difference Δt between the uplink and downlink reception times, expressed as:

[0089]

[0090] In the formula, This indicates the time of reception by satellite B during the uplink process; This indicates the time of reception by satellite A during the downlink process.

[0091] After removing outliers, the data is matched using formula (1), and the data that meet the conditions are a pair of bidirectional pseudorange data.

[0092] (2) Then perform inter-satellite relative clock error calculation:

[0093] In a specific exemplary technical solution, effective paired observation data is obtained after preprocessing. Since the ranging signal is of the same frequency and the signal propagation path is approximately symmetrical, the difference between the two-way pseudoranges can cancel out most of the channel error. However, there is still a propagation path asymmetry error caused by satellite motion, which needs to be corrected using orbit information. During time synchronization, it is necessary to normalize them to the same signal reception epoch. This can be achieved through polynomial interpolation or fitting of the pseudorange observations, commonly using Lagrange interpolation, etc. The two-way pseudorange satisfies:

[0094] ρ AB =c×(R) AB +t A -Δt+τ AB +r A )+ε AB

[0095] ρ BA =c×(R) BA +t B +Δt+τ BA+r B )+ε BA (2)

[0096] In the formula, ρ AB ρ BA These are the uplink and downlink pseudoranges, respectively; R AB R BA The geometric path delays for the uplink and downlink are respectively; c is the speed of light in vacuum; Δt is the relative clock difference between A and B; r A r B t A t B The transmit and receive delays of devices A and B, respectively, can be considered as stable invariants over a short period of time; τ AB τ BA These are other system errors in the uplink and downlink, mainly including ionospheric delay error, multipath effect error, antenna phase center error, relativistic effect error, motion delay, etc.; ε AB and ε BA It is random noise.

[0097] Taking the difference between equation (2), we can obtain the formula for solving the inter-satellite relative clock error:

[0098]

[0099] Equation (3) can be used to calculate the inter-satellite clock difference for each pair of satellites with a measurement link, but relevant system errors need to be corrected. Without considering epoch normalization error, the main system errors considered are motion delay and periodic relativistic effect delay, which need to be modeled and compensated according to the corresponding precision model.

[0100] The formulas for correcting motion delay and periodic relativistic effect delay are as follows:

[0101]

[0102] In the formula, Δt move For motion delay; Δt rel The time delay is due to periodic relativistic effects; c is the speed of light in a vacuum; r A r B These are the positions of A and B respectively; v A v B The velocities of A and B are respectively; t R t S These are the receiving and transmitting times of A and B, respectively.

[0103] In a specific exemplary technical solution of the present invention, step 2, the step of establishing a clock bias prediction combination model based on the navigation satellite clock bias obtained in step 1, includes:

[0104] The relative clock difference between the two satellites can be calculated using formula (3). When the atomic clock of one satellite is used as the master clock and its clock difference (deviation from the system time) is known, the clock difference of the other satellite can be obtained. If the master clock difference is temporarily set to zero, the relative clock difference obtained through inter-satellite time synchronization can be regarded as the clock difference of the other satellite.

[0105] Read the preprocessed clock error sequence and divide it into a training set (first 80%) and a test set (last 20%). Based on the clock error training set data, establish a clock error prediction combination model.

[0106] In a specific exemplary technical solution, trend term modeling includes:

[0107] The satellite clock bias fitting model uses a quadratic polynomial model, whose physical meaning corresponding to atomic clocks is clear, and the expression is as follows:

[0108] Δt(t i )=a0+a1(t i -t0)+a2(t i -t0) 2 +ε(t i (6)

[0109] In the formula, Δt i ti is the satellite clock bias (phase) at epoch i; t0 is the reference time for the star clock parameters; ti i ε represents the epoch time; a0, a1, and a2 represent the phase (clock difference), frequency (clock speed), and frequency drift rate (clock drift) of the reference time, respectively; ε represents the fitting error.

[0110] When at least three clock error data points are known, the parameters to be estimated and the fitting residuals can be obtained through the least squares method, and the clock error at any given time can then be predicted.

[0111] In a specific exemplary technical solution, periodic term modeling and extraction includes:

[0112] In the ISL clock difference observation scenario of BeiDou-3 satellites, inter-satellite time-frequency comparison data suffers from periodic or non-periodic gaps due to Earth obstruction, routing time slot planning, or equipment failures, resulting in irregular time intervals in the calculated relative clock difference sequence. Lomb-Scargle spectroscopy is used to extract the periodic term. LS spectroscopy is a power spectrum estimation method for non-uniformly sampled signals. It adaptively adjusts the frequency search grid by fitting a sinusoidal basis function using least squares. Because it does not require forced interpolation for missing data points but directly calculates the significance of each frequency point through weighted least squares, it avoids spurious frequency components introduced by interpolation, thus exhibiting good resistance to non-uniform sampling interference. The LS method mainly includes adaptive frequency analysis and harmonic regression modeling. The specific algorithm flow is as follows:

[0113] ① Construct a frequency network based on the Nyquist-Shannon sampling theorem, and set the frequency search range to be... Where T obs t represents the total observation duration. s This represents the median of the sampling interval. 1000 uniformly distributed frequency points are generated in logarithmic space to optimize high-frequency resolution.

[0114] ② For each frequency point f, the phase deviation caused by non-equidistant sampling is eliminated by using a phase correction function:

[0115]

[0116] In the formula, t i τ is the epoch time; τ(f) is the phase deviation corresponding to each frequency point.

[0117] ③ Calculate the power values ​​of the periodogram using the orthogonal basis projection method:

[0118]

[0119] In the formula, y i The residual is the result of fitting a quadratic polynomial to the clock error; σ 2 For y i The variance is used to ensure power normalization.

[0120] ④ To effectively extract significant periodic components f k Set the significance threshold to P. th =0.2×max(P(f)), automatically filtering out non-significant frequency components.

[0121] ⑤ Design Matrix:

[0122] X=[sin(2πf1t),cos(2πf1t),…,sin(2πf K t),cos(2πf K t)](9)

[0123] In the formula, f1, f2, ..., f K The significant periodic components were extracted.

[0124] ⑥ Solve for the parameters using the least squares method:

[0125]

[0126] In the formula, the default weight W = I.

[0127] ⑦ Based on the salient frequency f of the detection k Constructing a multiharmonic regression model:

[0128]

[0129] In the formula,

[0130] In the technical solution of this invention, firstly, gross errors in the inter-satellite link bidirectional pseudorange data are removed by preprocessing and effective data pairing is performed. Then, the relative clock error is calculated and modeled. A periodic term is introduced into the traditional QP model, and the main periodic components in the residual sequence are adaptively identified by Lomb-Scargle spectral analysis to solve the problem of periodic missed detection and false detection caused by discontinuity of ISL data. The periodic components are dynamically adjusted by a sliding window mechanism to avoid the introduction of historical noise by an excessively long window.

[0131] In a specific exemplary technical solution of this invention, the process of establishing a combined QP and LS model includes:

[0132] ① Fit the trend term to the training set data daily using a quadratic polynomial, and save the polynomial coefficients a0, a1, a2 of the last day;

[0133] ② Calculate the residual sequence and input it into LS periodic analysis to extract the main periodic components.

[0134] ③ Based on the QP model parameters obtained in step ①, substitute them into formula (6) to extrapolate the clock bias trend term for future times. It is worth noting that although the clock bias modeling result is optimal within the modeling time period, the clock bias reference term obtained by modeling is affected by the full arc data, and there may be some difference between it and the clock bias at the initial forecast time. This will cause a systematic deviation in the forecast clock bias, resulting in a decrease in short-term prediction accuracy. To compensate for this systematic error, the clock bias at the initial forecast time is extrapolated based on the clock bias change rate of the last 5 data in the training set, and this is used for calibration.

[0135] ④Based on the periodic term model obtained in step ②, substitute it into formula (11) to calculate the periodic term correction value within the prediction period;

[0136] ⑤ Result synthesis: The two components are linearly superimposed to obtain the final predicted value, which is then compared with the clock error data of the test set.

[0137] Please see Figures 2 to 5 In the specific exemplary technical solution of this invention, it is assumed that the clock bias of Beidou navigation satellites is determined and predicted based on the Chinese space station. The specific method and implementation steps are as follows:

[0138] 1) Data Acquisition:

[0139] Reference standard selected: BeiDou MEO satellite C19 (onboard rubidium clock);

[0140] Measurement target: MEO satellite (C21);

[0141] Data period: March 3-7, 2025 (cumulative days 62-66).

[0142] 2) Preprocessing procedure:

[0143] ① Outlier removal: The interquartile range (IQR) method is used to remove outliers;

[0144] ② Bidirectional pseudorange matching.

[0145] The preprocessed effective paired pseudorange data is obtained as follows: Figure 2 As shown.

[0146] 3) Modeling and forecasting steps:

[0147] ① The relative clock difference between satellites C19 and C21 is calculated using formula (3), and the trend term is fitted daily using a quadratic polynomial to obtain the fitting residuals. The results are as follows: Figure 3 As shown.

[0148] ② After removing the trend term using quadratic polynomial fitting, the residuals exhibit a certain periodicity. LS periodic analysis was performed on the residuals, and the main periodic components were extracted as 6.48h (relative intensity 1) and 13.06h (relative intensity 0.92). The harmonic fitting results are as follows: Figure 4 As shown.

[0149] ③ Using the quadratic polynomial coefficients and periodic term coefficients obtained in the above modeling process, the calculated relative clock bias is predicted, and the root mean square (RMS) and maximum absolute error (MaxAE) are statistically analyzed for different prediction durations for all satellite combinations. Taking the C19-C21 satellite combination data as an example, the 24-hour prediction results are as follows: Figure 5 As shown in the figure; the upper half of the figure is a comparison of the extrapolated 24-hour predictions of the two models, and the lower half of the figure is the distribution of the 24-hour prediction residuals of the two models.

[0150] In summary, for 3-hour predictions using the C19-C21 satellite combination, the QP model has an RMS value of 0.218 ns and a MaxAE value of 0.602 ns; the QP+LS model has an RMS value of 0.132 ns and a MaxAE value of 0.413 ns. For 24-hour predictions, the QP model has an RMS value of 0.518 ns and a MaxAE value of 1.665 ns; the QP+LS model has an RMS value of 0.450 ns and a MaxAE value of 1.457 ns.

[0151] The following are embodiments of the apparatus of the present invention, which can be used to execute embodiments of the method of the present invention. For details not disclosed in the apparatus embodiments, please refer to the embodiments of the method of the present invention.

[0152] Please see Figure 6 In this embodiment of the invention, a navigation satellite clock bias prediction system based on inter-satellite measurements is provided, comprising:

[0153] The data acquisition module is used to acquire navigation satellite clock bias.

[0154] The model building module is used to establish a clock bias prediction combination model based on the clock bias of the navigation satellites;

[0155] The clock error prediction module is used to obtain navigation satellite clock error prediction results for a selected time period in the future based on the clock error prediction combination model.

[0156] In the process of establishing the clock error prediction combination model, the trend term is first modeled using a quadratic polynomial, then the periodic term is modeled using the Lomb-Scargle spectral analysis method on the residual data, and finally the trend term modeling and periodic term modeling results are linearly superimposed to obtain the final clock error prediction combination model.

[0157] In one embodiment of the present invention, a computer device is provided, comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions in the computer storage medium to achieve a corresponding method flow or corresponding function. The processor described in this embodiment of the present invention can be used to execute the operation of a navigation satellite clock error prediction method based on inter-satellite measurements.

[0158] In one embodiment of the present invention, a storage medium is provided, specifically a computer-readable storage medium (memory), which is a memory device in a computer device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the computer device and extended storage media supported by the computer device. The computer-readable storage medium provides storage space that stores the operating system of the terminal. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be high-speed RAM (Random Access Memory) or non-volatile memory, such as at least one disk storage device. The processor can load and execute one or more instructions stored in the computer-readable storage medium to implement the corresponding steps of the navigation satellite clock bias prediction method based on inter-satellite measurements in the above embodiments.

[0159] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, etc.) containing computer-usable program code.

[0160] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0161] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0162] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0163] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A navigation satellite clock bias prediction method based on inter-satellite measurements, characterized in that, Includes the following steps: Obtain navigation satellite clock bias; Based on the clock bias of the navigation satellites, a clock bias prediction combination model is established; Based on the clock error prediction combination model, the navigation satellite clock error prediction results for a selected time period in the future are obtained; In the process of establishing the clock error prediction combination model, the trend term is first modeled using a quadratic polynomial, then the periodic term is modeled using the Lomb-Scargle spectral analysis method on the residual data, and finally the trend term modeling and periodic term modeling results are linearly superimposed to obtain the final clock error prediction combination model.

2. The navigation satellite clock bias prediction method based on inter-satellite measurements according to claim 1, characterized in that, In the clock difference prediction combination model The trend term is modeled as follows: Δt(t i )=a0+a1(t i -t0)+a2(t i -t0) 2 +ε(t i ); In the formula, Δt i t is the satellite clock bias at epoch i; t0 is the reference time for the star clock parameters; t i ε represents the epoch time; a0, a1, and a2 represent the phase, frequency, and frequency drift rate at the reference time, respectively; ε is the fitting error.

3. The navigation satellite clock bias prediction method based on inter-satellite measurements according to claim 1, characterized in that, In the clock difference prediction combination model, the periodic term modeling includes: A frequency network is constructed based on the Nyquist-Shannon sampling theorem, and the frequency search range is set to... Among them, T obs t represents the total observation duration. s The median of the sampling interval; For each frequency point f, the phase deviation caused by non-equal interval sampling is eliminated by the phase correction function, expressed as: In the formula, t i τ is the epoch time; τ(f) is the phase deviation corresponding to each frequency point; The power value of the periodogram is calculated using the orthogonal basis projection method, and the expression is: In the formula, y i The residual is the result of fitting the clock error quadratic polynomial; σ 2 For y i The variance; Based on the extracted significant periodic components f k Construct a multi-harmonic regression model, the expression of which is: In the formula, X=[sin(2πf1t),cos(2πf1t),…,sin(2πf K t),cos(2πf K t)]; In the formula, f1, f2, ..., f K W represents the weight of the extracted significant periodic components. Among them, in the significant periodic component f k During the extraction process, a significance threshold of P is set. th =0.2×max(P(f)) to filter out non-significant frequency components.

4. The navigation satellite clock bias prediction method based on inter-satellite measurements according to claim 1, characterized in that, In the step of obtaining navigation satellite clock bias The navigation satellite clock bias is the navigation satellite clock bias for a selected historical period before the ground operation and control service was interrupted; or, the navigation satellite clock bias is the calculated value or forecast result of the navigation satellite clock bias for a selected historical period after the ground operation and control service was interrupted.

5. The navigation satellite clock bias prediction method based on inter-satellite measurements according to claim 4, characterized in that, When the navigation satellite clock bias is the calculated value of the navigation satellite clock bias for a selected historical time period after the ground operation and control service is interrupted, the steps for obtaining the calculated value of the navigation satellite clock bias include: Based on the selected reference satellite, inter-satellite two-way time comparison measurements are performed to obtain the navigation satellite clock bias solution; among which, When performing inter-satellite two-way time comparison measurements, the following are included: First, the inter-satellite measurement data is preprocessed to obtain effective paired observation data; the preprocessing includes outlier removal and data pairing. Based on effective paired observation data, inter-satellite relative clock bias is calculated to obtain navigation satellite clock bias values.

6. A navigation satellite clock bias prediction system based on inter-satellite measurements, characterized in that, include: The data acquisition module is used to acquire navigation satellite clock bias. The model building module is used to establish a clock bias prediction combination model based on the clock bias of the navigation satellites; The clock error prediction module is used to obtain navigation satellite clock error prediction results for a selected time period in the future based on the clock error prediction combination model. In the process of establishing the clock error prediction combination model, the trend term is first modeled using a quadratic polynomial, then the periodic term is modeled using the Lomb-Scargle spectral analysis method on the residual data, and finally the trend term modeling and periodic term modeling results are linearly superimposed to obtain the final clock error prediction combination model.

7. A navigation satellite clock bias prediction system based on inter-satellite measurements according to claim 6, characterized in that, In the clock difference prediction combination model The trend term is modeled as follows: Δt(t i )=a0+a1(t i -t0)+a2(t i -t0) 2 +ε(t i ); In the formula, Δt i t is the satellite clock bias at epoch i; t0 is the reference time for the star clock parameters; t i ε represents the epoch time; a0, a1, and a2 represent the phase, frequency, and frequency drift rate at the reference time, respectively; ε is the fitting error.

8. A navigation satellite clock bias prediction system based on inter-satellite measurements according to claim 6, characterized in that, In the clock difference prediction combination model, the periodic term modeling includes: A frequency network is constructed based on the Nyquist-Shannon sampling theorem, and the frequency search range is set to... Among them, T obs t represents the total observation duration. s The median of the sampling interval; For each frequency point f, the phase deviation caused by non-equal interval sampling is eliminated by the phase correction function, expressed as: In the formula, t i τ is the epoch time; τ(f) is the phase deviation corresponding to each frequency point; The power value of the periodogram is calculated using the orthogonal basis projection method, and the expression is: In the formula, y i The residual is the result of fitting the clock error quadratic polynomial; σ 2 For y i The variance; Based on the extracted significant periodic components f k Construct a multi-harmonic regression model, the expression of which is: In the formula, X=[sin(2πf1t),cos(2πf1t),…,sin(2πf K t),cos(2πf K t)]; In the formula, f1, f2, ..., f K W represents the weight of the extracted significant periodic components. Among them, in the significant periodic component f k During the extraction process, a significance threshold of P is set. th =0.2×max(P(f)) to filter out non-significant frequency components.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the navigation satellite clock bias prediction method based on inter-satellite measurements as described in any one of claims 1 to 5.

10. A non-transitory 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 navigation satellite clock bias prediction method based on inter-satellite measurements as described in any one of claims 1 to 5.

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