Spaceborne clock stability evaluation method and device for sparse and irregular observations

Abstract

This application provides a method and apparatus for evaluating the stability of satellite-borne clocks under sparse and irregular observations, belonging to the field of time synchronization and satellite-borne clock measurement and evaluation technology. The method involves acquiring the sparse and irregularly distributed clock bias sequence of the satellite to be evaluated and mapping it to a unified time grid to obtain a network phase sequence, and constructing a discrete frequency sample sequence set and a set of available frequency sample indices. For each average time scale, the uncorrected Allan variance estimate under missing measurement conditions is calculated by taking the intersection of the forward and backward windows with the set of available frequency sample indices at each central index. A mixed correction factor is calculated using the mixed geometric bias correction factor, and the uncorrected Allan variance estimate is corrected using the mixed correction factor to obtain the corrected Allan variance. This invention can effectively eliminate the systematic bias introduced by missing measurement geometry, achieving accurate evaluation of satellite-borne clock stability under sparse and irregular observation conditions.

Description

Technical Field

[0001] This application belongs to the field of time synchronization and spaceborne clock measurement and evaluation technology, and specifically relates to a method and device for evaluating the stability of spaceborne clocks for sparse and irregular observations. Background Technology

[0002] Spaceborne clocks (such as atomic clocks and crystal oscillators) are key equipment in fields such as satellite navigation and deep space measurement, and their frequency stability directly affects the positioning and timing accuracy of the system. In the Global Navigation Satellite System (GNSS), the performance of spaceborne atomic clocks directly determines the positioning error, and accurately assessing their stability is of great engineering significance.

[0003] Existing clock alignment and time transfer technologies provide a variety of mature methods for spaceborne clock bias observation, mainly including Common-View (CV), All-View (AV), Two-Way Satellite Time and Frequency Transfer (TWSTFT), Precise Point Positioning (PPP), Orbit Determination and Time Synchronization (ODTS), Dual One-Way Microwave Time Transfer (DOWMTT), and Laser Time Transfer (LTT). Under ideal conditions such as good observation geometry, stable links, and continuous data, the above methods can obtain high-precision clock bias or equivalent frequency sequences, providing a reliable data foundation for stability analysis.

[0004] In stability assessment methods, Allan variance (Allan) and its variants, such as overlapped Allan variance, modified Allan variance, and Hadamard variance, are standard tools for analyzing the performance of clock and time-frequency links, and can characterize frequency noise characteristics through multi-scale sliding statistics. However, these methods implicitly rely on sampling premises of equal time intervals and continuous, uninterrupted measurements. In actual on-orbit operation, due to the influence of satellite line-of-sight windows, telemetry and control link scheduling, payload mode switching, and data transmission constraints, clock error observations are mostly sparse and irregular arc segment data, which disrupts the average window and covariance structure of standard Allan variances, introducing a systematic "geometric bias" caused by uneven sampling distribution. Interpolation and arc segment splicing, commonly used in engineering, introduce non-physical correlations and change the noise statistical structure, the effects of which are difficult to quantify and may even mask the true noise characteristics of the clock. Existing technologies cannot adapt to sparse and irregular observation scenarios, making it difficult to achieve accurate and objective assessment of onboard clock stability. Summary of the Invention

[0005] This application addresses the problem that the sparse and irregular distribution of clock difference sequences obtained from time comparison or transfer calculations leads to large biases in Allan variance estimation and unreliable stability assessments. It provides a method and apparatus for assessing the stability of spaceborne clocks for sparse and irregular observations.

[0006] To achieve the above objectives, this application adopts the following technical solution: Firstly, this application provides a method for evaluating the stability of spaceborne clocks for sparse and irregular observations, comprising the following steps: Obtain the sparse and irregularly distributed clock bias sequence of the satellite to be evaluated; The sparse and irregularly distributed clock bias sequence of the satellite to be evaluated is mapped to a unified time grid to obtain a network phase sequence, and a discrete frequency sample sequence set and an available frequency sample index set are constructed based on the network phase sequence. Based on the discrete frequency sample sequence set and the available frequency sample index set, for each average time scale, the uncorrected Allan variance estimate under the missing data condition is calculated by taking the intersection of the forward window and the backward window with the available frequency sample index set at each center index. Based on the missing geometry of the available frequency sample index set and the mixed noise model determined by the network phase sequence, the mixed geometry deviation correction factor is calculated. The mixed correction factor is calculated using the mixed geometric deviation correction factor. The uncorrected Allan variance estimate is then corrected using the mixed correction factor to obtain the corrected Allan variance, which is used as the evaluation result of the onboard clock stability.

[0007] Furthermore, obtaining the sparse and irregularly distributed clock bias sequence of the satellite to be evaluated specifically includes: Collect observation data of the satellite to be evaluated and ground stations and / or observation satellites within the visible arc, and obtain auxiliary data sets; Using the observation data and the auxiliary data set, the clock difference sequence of the satellite to be evaluated is obtained through clock comparison or time transfer calculation; The median absolute deviation method is used to detect and remove gross errors in the clock difference sequence of the satellite to be evaluated, thereby obtaining a sparse and irregularly distributed clock difference sequence of the satellite to be evaluated.

[0008] Further, the step of mapping the sparse and irregularly distributed clock bias sequence of the satellite to be evaluated to a unified time grid to obtain a network phase sequence, and constructing a discrete frequency sample sequence set and an available frequency sample index set based on the network phase sequence includes: A unified time grid is constructed using a preset reference sampling interval; The sparse and irregularly distributed clock difference sequence of the satellite to be evaluated is mapped onto the unified time grid to obtain the network phase sequence, wherein the network points without observation are marked as missing measurements; Traverse all adjacent grid points in the network phase sequence. When both adjacent grid points have observations, construct discrete frequency samples based on the phase difference between the adjacent grid points to obtain a set of discrete frequency sample sequences. Record the grid point location indices of all constructed discrete frequency samples as a set of available frequency sample indices.

[0009] Further, the step of calculating the uncorrected Allan variance estimate under the missing data condition based on the discrete frequency sample sequence set and the available frequency sample index set, for each average time scale, by taking the intersection of the forward window and the backward window with the available frequency sample index set at each center index, includes: For any center index, define the intersection of the forward window and the backward window on the set of available frequency sample indices; When both the forward window and the backward window are not empty, calculate the mean of the discrete frequency samples within the corresponding window respectively; A three-point difference value is constructed based on the mean of the discrete frequency samples within the window; All central indices that can participate in the statistics are counted to form a central index set and the number of central index sets is calculated. The uncorrected Allan variance estimate is then calculated based on the three-point difference value and the number of central index sets.

[0010] Furthermore, the hybrid noise model determined by the network phase sequence includes at least two of white phase modulation noise, white frequency modulation noise, and random walk frequency modulation noise; The process of determining the mixed noise model from the network phase sequence is as follows: Based on the network phase sequence, a full ergodic three-point difference calculation is performed on the average factor corresponding to all average time scales to obtain a dense scatter dataset. Logarithmically bin the dense scatter dataset, and take a weighted average of the three-point difference calculation results within each bin to obtain a representative point set; Robust fitting is performed on the representative point set to obtain the fitting coefficients for white phase modulation noise, white frequency modulation noise and random walk frequency modulation noise respectively. Based on the fitting coefficients, the contribution values ​​of white phase modulation noise, white frequency modulation noise, and random walk frequency modulation noise at each average time scale are calculated, and the contribution values ​​are normalized to obtain the mixed noise weights, thereby determining the mixed noise model.

[0011] Furthermore, based on the missing geometry of the available frequency sample index set and the mixed noise model determined by the network phase sequence, the process of calculating the mixed geometry bias correction factor is as follows: The missing geometry of the available frequency sample index set is fixed; After obtaining the mixed noise weights, the mixed geometric deviation correction factor is calculated using analytical formulas or Monte Carlo simulation.

[0012] Further, the process of calculating a mixed correction factor using the mixed geometric deviation correction factor, correcting the uncorrected Allan variance estimate using the mixed correction factor, and obtaining the corrected Allan variance as the result of the onboard clock stability assessment specifically includes: The mixed correction factor is calculated using the aforementioned mixed geometric deviation correction factor; Multiply the uncorrected Allan variance estimate by the mixed correction factor to obtain the corrected Allan variance; The corrected Allan variance is output as the satellite clock stability evaluation result.

[0013] Secondly, this application provides a satellite clock stability evaluation system for sparse and irregular observations, used to implement a satellite clock stability evaluation method for sparse and irregular observations, including: The ground operation and control system includes a ground operation and control center and at least one ground station, which is used for link planning, command issuance and observation data aggregation; The satellite to be evaluated carries an onboard clock, which is used to establish links with ground stations and observation satellites and to perform measurements. An observation satellite is used to establish an inter-satellite link with the satellite to be evaluated and to perform measurements. The data processing and evaluation module, deployed at the ground control center or the satellite to be evaluated, includes: The data acquisition module is used to acquire the sparse and irregularly distributed clock difference sequence of the satellite to be evaluated; The gridding and frequency construction module is used to map the sparse and irregularly distributed clock difference sequence of the satellite to be evaluated to a unified time grid to obtain a network phase sequence, and construct a discrete frequency sample sequence set and an available frequency sample index set based on the network phase sequence. The missing Allan variance estimation module is used to calculate the uncorrected Allan variance estimate under missing conditions based on the discrete frequency sample sequence set and the available frequency sample index set for each average time scale by taking the intersection of the forward window and the backward window with the available frequency sample index set at each center index. The correction factor calculation module is used to calculate the mixed geometry deviation correction factor based on the missing geometry of the available frequency sample index set and the mixed noise model determined by the network phase sequence. The correction module is used to calculate the mixed correction factor using the mixed geometric deviation correction factor, and then correct the uncorrected Allan variance estimate using the mixed correction factor to obtain the corrected Allan variance, which is used as the evaluation result of the onboard clock stability.

[0014] Thirdly, this application provides a computer device, including: a processor and a computer-readable storage medium; A processor, adapted to execute computer programs; A computer-readable storage medium storing a computer program, which, when executed by the processor, implements a method for evaluating the stability of a satellite clock for sparse and irregular observations.

[0015] Fourthly, this application provides a computer-readable storage medium storing a computer program adapted to be loaded by a processor and executed as a method for evaluating the stability of a satellite clock for sparse and irregular observations.

[0016] Compared with the prior art, this application has the following beneficial effects: This application provides a method for evaluating the stability of spaceborne clocks under sparse and irregular observations. Compared with the standard Allan variance estimation method in the prior art that relies on the assumption of continuous and equal-interval sampling, this invention constructs a complete adaptive evaluation framework for missing data under sparse and irregular observation conditions. Existing methods, when faced with missing data, disrupt the averaging process of the fixed window, significantly reduce the number of available center points, and cause the statistics of different center points to become out of sync, leading to systematic biases in the estimation results. Furthermore, commonly used interpolation point supplementation or arc segment splicing methods in engineering introduce non-physical correlations, altering the noise statistical structure. This invention maps sparse and irregularly distributed clock difference sequences to a unified time grid and marks missing data. Based on this, and using a set of discrete frequency sample sequences and a set of available frequency sample indices, the intersection of the forward and backward windows with the set of available frequency sample indices is taken at each center index. This allows for the full utilization of available samples to calculate the uncorrected Allan variance estimate even on a set of discrete frequency sample sequences with multiple arc segments and sparse missing data. Furthermore, this invention calculates a mixed geometric bias correction factor based on the missing geometry and a mixed noise model determined by the network phase sequence, and corrects the uncorrected Allan variance estimate, effectively eliminating the systematic bias introduced by uneven sampling time distribution. The above technical solutions work together to obtain near-perfect stability assessment results under sparse and irregular observation conditions, without interpolation or splicing, thus solving the problem of large Allan variance estimation bias and unreliable stability assessment caused by sparse and irregular observations in existing technologies. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating the method for evaluating the stability of spaceborne clocks for sparse and irregular observations according to the present invention.

[0019] Figure 2 This is a schematic diagram of the composition structure of the spaceborne clock stability evaluation system for sparse and irregular observations according to the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0021] like Figure 1 As shown, this application provides a method for evaluating the stability of spaceborne clocks for sparse and irregular observations, including the following steps: S1, Obtain the sparse and irregularly distributed clock difference sequence of the satellite to be evaluated; In one specific implementation, this step is achieved through the following process: Collect observation data of the satellite to be evaluated, ground stations, and / or observation satellites within the visible arc, and obtain auxiliary data sets.

[0022] Specifically, link visibility analysis and link establishment planning are carried out: collect parameter information of ground stations and satellites, including the location of ground stations, orbit data, and communication frequency bands, and combine environmental factors such as terrain obstruction and atmospheric interference to calculate the visibility windows and link coverage between ground stations and satellites, and between satellites. Based on the comprehensive visibility situation, design communication priorities and switching sequences, and produce link establishment planning documents.

[0023] Link establishment execution and two-way observation data acquisition: The ground control system parses the link establishment planning document to generate specific operation instructions, including the timing operations for link establishment, switching, and closure, and uploads the instructions to the satellite. After receiving the instructions, the satellite executes the satellite-to-ground or inter-satellite link establishment operations step by step, and the ground monitors the link status in real time.

[0024] After establishing a link between the satellite and ground stations or between satellites, observational data for clock bias calculation is collected within the visible arc of the satellite to be evaluated, according to a preset observation system. When the satellite to be evaluated establishes a link with a ground station, one-way and / or two-way observation data are collected. This data includes single-frequency or multi-frequency pseudorange observations and / or carrier phase observations. The transmission and reception timestamps, operating frequency band, signal system, link direction, and observation quality indicators for each observation data point are recorded, forming a satellite-ground observation set. When the satellite to be evaluated establishes a link with an observation satellite, one-way and / or two-way inter-satellite observation data are collected. This data includes single-frequency or multi-frequency pseudorange observations and / or carrier phase observations. The link direction, timetamps, frequency band system, and observation quality indicators are recorded, forming an inter-satellite observation set. Satellite-ground and inter-satellite observations are classified and formatted according to observation type, link direction, and frequency band system, with standardized data units and time stamping methods, forming a standardized observation dataset. When both satellite-ground and inter-satellite observations exist simultaneously, they are merged to form a fused observation dataset.

[0025] The satellite-to-ground observation combination between the satellite to be evaluated and the ground station is transmitted to the ground control center or the satellite to be evaluated. The inter-satellite observation combination between the satellite to be evaluated and the observation satellite is also transmitted to the ground control center or the satellite to be evaluated.

[0026] A set of auxiliary data, using the same time scale and coordinate reference as the observation data, is acquired from the ground control center or the satellite to be evaluated. This auxiliary data set includes: orbit and velocity information (acquiring the orbital position and velocity information of the satellite to be evaluated and related observation terminals, unified to a predetermined reference coordinate system); reference terminal time scale information (acquiring the clock difference parameters of the local clock at the ground station relative to the system reference time scale, or acquiring the clock difference parameters of the local clock of the observed satellite relative to the system reference time scale); propagation and environmental correction parameters (acquiring ionospheric correction, tropospheric correction, relativistic correction parameters, and time system conversion parameters); and equipment and link calibration parameters (acquiring calibration parameters such as hardware delay at the transmitter and receiver, antenna phase center delay, and cable delay).

[0027] Integrate all observation data of the satellite to be evaluated, ground stations, and observation satellites within the visible link arc at the ground control center or on the satellite to be evaluated, and combine them with auxiliary data sets to calculate the clock difference sequence of the satellite to be evaluated using clock comparison or time transfer technology.

[0028] The Median Absolute Deviation (MAD) method was used to detect and remove outliers in the clock bias sequence of the satellite to be evaluated, resulting in a sparse and irregularly distributed clock bias sequence of the satellite to be evaluated.

[0029] The formula for calculating the absolute deviation of the median is:

[0030] in, MAD This represents the absolute deviation of the median. For the first Clock difference value, The median of the clock bias sequence of the satellite to be evaluated. For the median operator, if Then it can be considered 'b' represents the gross error and removes it; 'b' is the gross error determination coefficient. This step avoids the non-physical correlations introduced by interpolation or arc segment splicing in the background techniques by preserving the original missing characteristics of the observation data.

[0031] S2, the sparse and irregularly distributed clock difference sequence of the satellite to be evaluated is mapped to a unified time grid to obtain a network phase sequence. Based on the network phase sequence, a discrete frequency sample sequence set and an available frequency sample index set are constructed. The network phase sequence refers to the time sequence composed of phase values ​​obtained at each grid node after mapping the sparse and irregularly distributed clock difference sequence of the satellite to be evaluated to a unified time grid constructed by a preset reference sampling interval in chronological order. The term "network" specifically refers to an abstract time grid structure composed of equally spaced time points. Each grid node corresponds to a fixed time point. This unified time grid covers the entire observation time range, and time points without observations are marked as missing measurements.

[0032] In one specific implementation, this step is achieved through the following process: Using a preset reference sampling interval Building a unified time grid The sparse and irregularly distributed clock bias sequences of the satellites to be evaluated are mapped onto a unified time grid to obtain the network phase sequence. In the unified time grid, network points without observations are marked as missing measurements.

[0033] Iterate through all adjacent grid points in the network phase sequence, when two adjacent grid points... and When observations exist for all grid points, a discrete frequency sample is constructed based on the phase difference between adjacent grid points:

[0034] in, For the first A discrete frequency sample, and Given the phase values ​​of two adjacent grid points, a set of discrete frequency sample sequences is obtained by traversing all adjacent available grid points. Record the grid point location indices of all constructed discrete frequency samples as a set of available frequency sample indices. This step preserves the sparse and irregular characteristics of the sparse and irregularly distributed clock difference sequences of the satellite to be evaluated by marking missing data. At the same time, it constructs a set of discrete frequency sample sequences and a set of available frequency sample indices, which solves the problem that the standard Allan variance estimator relies on the assumption of equal time intervals and continuous sampling.

[0035] S3, Based on the discrete frequency sample sequence set and the available frequency sample index set, for each average time scale, the uncorrected Allan variance estimate under the missing data condition is calculated by taking the intersection of the forward window and the backward window with the available frequency sample index set at each center index. In one specific implementation, this step is achieved through the following process: For any central index Define the intersection of the forward and backward windows on the set of available frequency sample indices; for the average factor m (corresponding to the average time scale) The forward window intersection is defined as:

[0036] Backward window intersection is defined as:

[0037] in, This is the set of available frequency sample indices. If or If it is empty, then discard the central index. .

[0038] When both the forward and backward windows are not empty, calculate the mean of the discrete frequency samples within the corresponding windows:

[0039]

[0040] in, and These represent the number of valid samples within the forward window and the backward window, respectively. For the first A discrete frequency sample.

[0041] Construct a three-point difference value based on the mean of discrete frequency samples within the window:

[0042] Statistical analysis of all central indexes that can participate in the statistics This constitutes the central index set. The number of index sets in the statistics center :

[0043]

[0044] And based on the three-point difference values ​​and the number of central index sets, the uncorrected Allan variance estimate under the missing test condition is calculated:

[0045] In the formula,

[0046]

[0047] in, The average time scale is The uncorrected Allan variance estimate at that time. Let covariance be the set of discrete frequency sample sequences. The weight vector of the forward window. The weight vector of the backward window. Weight vector The One element, Weight vector The One element, Let T represent the weight vector or difference vector corresponding to the nth center index and the mean factor being m, where T is the transpose of the vector. This represents the squared increment within the window.

[0048] This step achieves full utilization of available samples on a set of discrete frequency sample sequences with multiple arc segments and sparse missing measurements by taking the intersection of the forward and backward windows with the set of available frequency sample indices at each central index. This eliminates the need for interpolation or splicing and solves the problem of the fixed window averaging process being disrupted and the estimation results being subject to systematic bias due to missing measurements.

[0049] S4. Based on the missing geometry of the available frequency sample index set and the mixed noise model determined by the network phase sequence, the mixed geometry bias correction factor is calculated. The missing geometry refers to the distribution pattern of missing values ​​in the observation data, specifically manifested as the sampling point location, missing interval length, missing interval distribution density, and length and interval characteristics of the available arc segments defined by the available frequency sample index set. In one specific implementation, the core problem addressed in this step is that the systematic bias caused by missing geometry needs to be corrected in conjunction with the actual clock noise characteristics. However, actual clock noise is typically a mixture of multiple components, including white phase modulation, white frequency modulation, and random walk frequency modulation. A single noise correction model cannot adapt to this characteristic, leading to inaccurate bias correction. This step ensures the adaptability of the mixed geometric bias correction factor under different average time scales by accurately constructing a mixed noise model. The mixed noise model includes at least two of the following: white phase modulation, white frequency modulation, and random walk frequency modulation. The specific implementation steps are as follows: The hybrid noise model determined by the network phase sequence includes at least two of white phase modulation (WPM), white frequency modulation, and random walk frequency modulation; Based on network phase sequence (missing data marked as NaN) and reference sampling interval The average factor corresponding to all average time scales ( ≥1) Perform a full traversal of the three-point difference calculation: for each central index If all three points exist simultaneously (i.e. none are missing), then perform three-point differencing. calculate:

[0050] in, For time The corresponding phase observation value is the starting point of the current calculation window; For time ( ) The corresponding phase observation value is the center point of the current calculation window; For time ( ) The corresponding phase observation value is the center point of the current calculation window.

[0051] For each average factor corresponding to all average time scales By taking the mean square of all valid three-point terms, we obtain the Allen variance estimate based on the three-point difference:

[0052]

[0053] in, This represents the three-point difference Allen variance. This represents the three-point difference Allan bias. This indicates that the average value is taken over all valid three-point items. Indicates the average time scale.

[0054] At the same time, the statistics The number of three items available below (i.e., the starting index that satisfies the condition that all three points exist) The number of points (indicated by the number of points) is used as a quantitative indicator of the statistical confidence level of that point. This yields a dense scatter plot dataset. Used for subsequent estimation of mixed noise weights.

[0055] To avoid dense scatter points being too dense at certain time scales and different The large difference in the number of valid three points leads to unstable fitting, according to the dense scatter dataset. Logarithmic binning is performed, and within each bin... Perform a weighted average, with the weights selected first. Points with more than three valid points have larger weights, resulting in a representative set of points for fitting. ,in, The average time scale after merging. The weights are for the weighted average. This represents the combined Allen bias.

[0056] In the Allen variance domain, robustly fit the fitting coefficients of white phase modulation noise, white frequency modulation noise, and random walk frequency modulation noise onto the representative point set, making them approximate the following form:

[0057] in Represents the Allen variance curve. The amplitude coefficient representing the white phase modulation noise (WPM) is used. The amplitude coefficient representing white frequency modulation noise (WFM) The amplitude coefficient representing the random walk frequency modulation noise (RWFM) is... Corresponding to the white phase modulation noise contribution, Corresponding to the white frequency modulation noise contribution, The corresponding random walk frequency modulation noise contribution.

[0058] After obtaining the fitting coefficients Then, the white phase modulation noise at each average time scale is calculated. White frequency modulation noise and random walk frequency modulation noise Contribution value:

[0059]

[0060]

[0061] The contribution values ​​of the above three components are normalized to obtain the mixed noise weights. :

[0062]

[0063] Among the noise components j ∈{WPM,WFM,RWFM}, from which we can obtain the average time scales. Mixed noise weights This forms the final mixed noise model.

[0064] In one specific implementation, the process of calculating the mixed geometry bias correction factor based on the missing geometry of the available frequency sample index set and the mixed noise model determined by the network phase sequence is as follows: The missing geometry of a fixed available frequency sample index set reflects the sparse and irregular distribution characteristics of the observed data. The mixed noise weights are obtained. The mixed geometric deviation correction factor is calculated using either analytical formulas or Monte Carlo simulation. .

[0065] Hybrid geometric deviation correction factor Defined as:

[0066] in, This indicates that under complete and continuous observation conditions, the first... j Allan variance corresponding to noise type; This indicates that under conditions of missing or sparse observations, the first... j Allan variance corresponding to noise class.

[0067] The specific process of using the analytical formula calculation method is as follows: The mixed noise consists of white phase modulation noise, white frequency modulation noise, and random walk frequency modulation noise, and the relative contribution of each component in the Allan variance domain can be determined by the mixed noise weights. Under the given conditions, the mixed geometric deviation correction factor Written in a closed form as a weighted harmonic fusion:

[0068] in, The weights are the renormalized weights for the effective components and the noise components. j∈{WPM,WFM,RWFM}, Noise component j The variance scaling correction factor under the current missing-measure geometry is defined as:

[0069] in, Represents the average time scale under complete data conditions. First j The difference in mean and variance of the frequencies of two samples of noise-like objects; Indicates the average time scale under conditions of missing data. First j The difference between the mean and variance of the frequencies of two samples of noise type The average factor is Construct the weight vector or difference template vector of the three-point difference of the Allan variance.

[0070] For the three types of noise, their covariance matrix The specific calculations for each element are as follows:

[0071] Where p and q represent the row and column indices of the elements in the covariance matrix. ; , and The Kronecker function; The standard deviation of the white phase-modulated white noise component in the phase sequence; This represents the standard deviation of the discrete frequency sample sequence corresponding to the phase sequence. This represents the standard deviation of the white noise increment driving the random walk in random walk frequency modulation.

[0072] The specific process of using the Monte Carlo simulation method is as follows: Under the condition of missing measurement masking consistent with the actual data distribution, R simulations were performed to generate discrete frequency sample sequence sets for three types of noise: white phase modulation noise, white frequency modulation noise, and random walk frequency modulation noise, and the full sampling Allan variance was calculated. Missing test Allan variance after applying the same missing test mask Thus, the single-noise Monte Carlo correction factor, i.e., the mixed geometric deviation correction factor, is obtained. :

[0073] Where r represents the index of a single simulation.

[0074] It should be noted that missing data geometry refers to the spatial distribution and statistical characteristics of missing data in the phase sequence, while missing data mask conditions refer to constraints composed of binary masks that are completely consistent with the missing data distribution of the actual network phase sequence. These constraints are used in Monte Carlo simulations to simulate the impact of the missing data patterns of real data on Allan variance estimation.

[0075] The hybrid geometric deviation correction factor It is only related to the missing geometry and noise type, and can be pre-calculated offline to form a lookup table for quick online retrieval.

[0076] S5. The mixed correction factor is calculated using the mixed geometric deviation correction factor. The uncorrected Allan variance estimate is corrected using the mixed correction factor to obtain the corrected Allan variance, which is used as the evaluation result of the satellite clock stability.

[0077] Hybrid geometric deviation correction factor Combined with mixed noise weights The weighted harmonic fusion method is used to obtain the hybrid correction factor, which is calculated as follows:

[0078] Output mixing correction factor: The calculated hybrid correction factor This is used to correct the uncorrected Allan variance estimate, resulting in the corrected Allan variance. :

[0079] The corrected Allen variance The output is the evaluation result of the onboard clock stability.

[0080] Example 1 This embodiment assesses the stability of sparse and irregular clock biases under two-way microwave measurements between a space station and the ground. Using a low-Earth orbit space station platform as the evaluation carrier, observation data is acquired through two-way microwave measurements to verify the effectiveness of the onboard clock stability assessment method for sparse and irregular observations provided in this application.

[0081] The space station carries an onboard clock, an onboard global navigation satellite system receiver, a space-to-ground time and frequency transfer payload, and a space data transmission module. The ground terminal includes a ground operations control center and several ground stations, each equipped with a stable frequency standard and a timekeeping system.

[0082] Since the orbital period of the low-orbit platform is about 90 minutes, the visible window for each track at a single station is usually only a few minutes. Therefore, the clock difference observation sequence exhibits a sparse and irregular characteristic with short usable arc segments and long gaps between arc segments.

[0083] The ground control center calculates the visual windows between the space station and various ground stations, generates link establishment planning documents, and distributes them. Within each visual arc, after the space-to-ground link is established, the payload collects uplink and downlink observation data (pseudorange and carrier phase) and records auxiliary information such as transmission time, reception time, frequency band, link direction, signal-to-noise ratio, lock status, and cycle slip markers. The observation data is transmitted back via data transmission and aggregated at the ground control center.

[0084] Using a preset reference sampling interval A unified time grid is constructed every 30 seconds. The sparse and irregularly distributed clock difference sequence is mapped onto the unified time grid to obtain the network phase sequence, where network points without observations are marked as missing measurements.

[0085] Traverse all adjacent grid points in the network phase sequence. When both adjacent grid points have observations, construct discrete frequency samples based on the phase difference between the adjacent grid points to obtain a set of discrete frequency sample sequences. Record the grid point position indices of all constructed discrete frequency samples as a set of available frequency sample indices.

[0086] Based on the set of discrete frequency sample sequences and the set of available frequency sample indices, for each average time scale and for any center index, the intersection of the forward window and the backward window on the set of available frequency sample indices is defined: The forward window intersection is defined as:

[0087] Backward window intersection is defined as:

[0088] or When all are non-empty, calculate the mean of the discrete frequency samples within the corresponding window, construct a three-point difference value based on the mean of the discrete frequency samples within the window, count all the center index sets that can participate in the statistics, count the number of the center index sets, and calculate the uncorrected Allan variance estimate based on the three-point difference value and the number of center index sets.

[0089] Based on the network phase sequence, a full ergodic three-point difference calculation is performed on the average factor corresponding to all average time scales. For each central index, if all three points exist simultaneously, a three-point difference calculation is performed; the mean square of all valid three-point terms under the average factor corresponding to all average time scales is taken to obtain the Allan variance estimate based on the three-point difference. Logarithmically binning is performed on the dense scatter dataset. Within each bin, the three-point difference calculation results are weighted and averaged to obtain a representative set of points. Robust fitting is then performed on the representative set of points to obtain the fitting coefficients for white phase modulation noise, white frequency modulation noise, and random walk frequency modulation noise. Based on the fitting coefficients, the contribution values ​​of white phase modulation noise, white frequency modulation noise and random walk frequency modulation noise are calculated at each average time scale. The contribution values ​​are normalized to obtain the mixed noise weights, and the final mixed noise model is constructed based on the mixed noise weights.

[0090] For the missing geometry of the fixed available frequency sample index set, after obtaining the mixed noise weights, the mixed geometry deviation correction factor is calculated using an analytical formula.

[0091] The mixed correction factor is calculated using the mixed geometric deviation correction factor. The uncorrected Allan variance estimate is then corrected using the mixed correction factor to obtain the corrected Allan variance, which is used as the evaluation result of the onboard clock stability.

[0092] In this embodiment, the above steps are performed by the data processing and evaluation module deployed in the ground operation and control center.

[0093] Example 2 The difference between this embodiment and Embodiment 1 lies in the observation link.

[0094] The space station carries an onboard clock, an onboard global navigation satellite system receiver, a time and frequency transfer payload, and a space data transmission module. The BeiDou observation satellite carries an onboard clock and a time and frequency transfer payload to establish inter-satellite links with the space station. A ground control system is configured, comprising a ground control center and several ground stations.

[0095] The ground control system calculates the visible window between the space station and the BeiDou observation satellites, generates and distributes the link establishment planning document. Within each visible arc, after the inter-satellite link is established, the time-frequency transfer payload collects bidirectional inter-satellite observation data, including pseudorange and carrier phase observations, and records the time stamps for transmission and reception, operating frequency band, signal system, link direction, and observation quality indicators. The observation data is transmitted back via the space data transmission module and aggregated at the ground control center.

[0096] The ground control system acquires auxiliary data sets in parallel, including: orbit and velocity information of the space station and BeiDou observation satellites, clock difference parameters of the BeiDou observation satellites' local clocks relative to the system reference time scale, motion delay correction parameters, relativistic correction parameters, atmospheric delay correction parameters, and hardware delay calibration parameters. Subsequently, the ground control center fuses the observation data and auxiliary data sets, and obtains the clock difference sequence of the satellites to be evaluated on the space station through clock comparison or time transfer calculation.

[0097] The median absolute deviation method is used to detect and remove gross errors in the clock difference sequence of the satellite to be evaluated, thereby obtaining a sparse and irregularly distributed clock difference sequence of the satellite to be evaluated.

[0098] The subsequent steps are the same as in Example 1, sequentially performing gridding and frequency sample construction, uncorrected Allan variance estimation under missing measurement conditions, determination of mixed noise model and calculation of mixed geometric deviation correction factor, correction and output, and finally obtaining the space station onboard clock stability curve.

[0099] Example 3 This embodiment enables both ground-to-satellite and inter-satellite observation.

[0100] The space station carries an onboard clock, a global navigation satellite system receiver, a time and frequency transfer payload, and a space data transmission module. The ground terminal is equipped with a ground control system, which includes a ground control center and several ground stations. The BeiDou observation satellite carries an onboard clock and a time and frequency transfer payload to establish inter-satellite links with the space station.

[0101] The ground-to-satellite observation data and inter-satellite observation data are aligned and formatted according to a unified time label and reference time scale to form a standardized observation combination dataset, which is then merged to form a fused observation dataset.

[0102] The ground control system integrates all observation data from the space station, ground stations, and BeiDou observation satellites within the visible link arc, and combines them with auxiliary data sets to obtain the sparse and irregular clock difference sequence of the satellites to be evaluated on the space station through clock comparison or time transfer calculation.

[0103] The median absolute deviation method is used to detect and remove outliers in the clock difference sequence, resulting in a sparse and irregularly distributed clock difference sequence. The median absolute deviation method is used to detect and remove gross errors in the clock difference sequence of the satellite to be evaluated, thereby obtaining a sparse and irregularly distributed clock difference sequence of the satellite to be evaluated.

[0104] The subsequent steps are the same as in Example 1, sequentially performing gridding and frequency sample construction, uncorrected Allan variance estimation under missing measurement conditions, determination of mixed noise model and calculation of mixed geometric deviation correction factor, correction and output, and finally obtaining the space station onboard clock stability curve.

[0105] In the above embodiments, each step can be deployed at a ground control center or on-board processing unit. The preset reference sampling interval, the threshold coefficient of the median absolute deviation method, and the number of Monte Carlo simulations can be selected based on the observation duty cycle, noise level, and computational resources. When the number of effective centers is insufficient, computability and stability can be improved by fusing observations or adjusting the reference sampling interval.

[0106] This application does not limit the observation link system and data source. In addition to two-way links between the space station and the ground or between satellites, it is also applicable to the stability evaluation of sparse and irregular clock difference sequences obtained by methods such as satellite common view method, satellite all-view method, precise single-point positioning method, and precise orbit determination and time synchronization method.

[0107] In one embodiment, such as Figure 2 As shown, this application provides a satellite clock stability assessment system for sparse and irregular observations, which includes a ground control system, the satellite to be assessed, the observation satellite, and a data processing and assessment module.

[0108] The ground operation and control system includes a ground operation and control center and at least one ground station, which is used for link planning, command issuance and observation data aggregation; The satellite to be evaluated carries an onboard clock for establishing links with ground stations and observation satellites and performing measurements. The satellite to be evaluated also includes: an onboard global navigation satellite system receiver for providing the satellite's position, velocity and coarse time reference; a time and frequency transmission payload for collecting observation data required for clock error calculation; and a space data transmission module for transmitting observation data back and receiving commands. An observation satellite is used to establish an inter-satellite link with the satellite to be evaluated and to perform measurements. A data processing and evaluation module, deployed at the ground control center or the satellite to be evaluated, is used to execute a satellite-borne clock stability evaluation method for sparse and irregular observations as proposed in this application, including: The data acquisition module is used to acquire the sparse and irregularly distributed clock difference sequence of the satellite to be evaluated; The gridding and frequency construction module is used to map the sparse and irregularly distributed clock difference sequence of the satellite to be evaluated to a unified time grid to obtain a network phase sequence, and construct a discrete frequency sample sequence set and an available frequency sample index set based on the network phase sequence. The missing Allan variance estimation module is used to calculate the uncorrected Allan variance estimate under missing conditions based on the discrete frequency sample sequence set and the available frequency sample index set for each average time scale by taking the intersection of the forward window and the backward window with the available frequency sample index set at each center index. The correction factor calculation module is used to calculate the mixed geometry deviation correction factor based on the missing geometry of the available frequency sample index set and the mixed noise model determined by the network phase sequence. The correction module is used to calculate the mixed correction factor using the mixed geometric deviation correction factor, and then correct the uncorrected Allan variance estimate using the mixed correction factor to obtain the corrected Allan variance, which is used as the evaluation result of the onboard clock stability.

[0109] In one embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method described above.

[0110] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method.

[0111] The various embodiments in this specification are described in a progressive manner. For directly identical or similar parts of the embodiments, refer to each other. Each embodiment focuses on its differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. It should be noted that the technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification.

[0112] The embodiments described above are merely preferred embodiments of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various improvements and substitutions without departing from the technical principles of this application, and these improvements and substitutions should also be considered within the scope of protection of this application. Therefore, the scope of protection of this patent application should be determined by the scope of the claims.

Claims

1. A method for evaluating the stability of a spaceborne clock for sparse and irregular observations, characterized in that, Includes the following steps: Obtain the sparse and irregularly distributed clock bias sequence of the satellite to be evaluated; The sparse and irregularly distributed clock bias sequence of the satellite to be evaluated is mapped to a unified time grid to obtain a network phase sequence, and a discrete frequency sample sequence set and an available frequency sample index set are constructed based on the network phase sequence. Based on the discrete frequency sample sequence set and the available frequency sample index set, for each average time scale, the uncorrected Allan variance estimate under the missing data condition is calculated by taking the intersection of the forward window and the backward window with the available frequency sample index set at each center index. Based on the missing geometry of the available frequency sample index set and the mixed noise model determined by the network phase sequence, the mixed geometry deviation correction factor is calculated. The mixed correction factor is calculated using the mixed geometric deviation correction factor. The uncorrected Allan variance estimate is then corrected using the mixed correction factor to obtain the corrected Allan variance, which is used as the evaluation result of the onboard clock stability.

2. The method for evaluating the stability of a spaceborne clock for sparse and irregular observations according to claim 1, characterized in that, Obtaining the sparse and irregularly distributed clock bias sequence of the satellite to be evaluated specifically includes: Collect observation data of the satellite to be evaluated and ground stations and / or observation satellites within the visible arc, and obtain auxiliary data sets; Using the observation data and the auxiliary data set, the clock difference sequence of the satellite to be evaluated is obtained through clock comparison or time transfer calculation; The median absolute deviation method is used to detect and remove gross errors in the clock difference sequence of the satellite to be evaluated, thereby obtaining a sparse and irregularly distributed clock difference sequence of the satellite to be evaluated.

3. The method for evaluating the stability of a spaceborne clock for sparse and irregular observations according to claim 1, characterized in that, The steps of mapping the sparse and irregularly distributed clock bias sequence of the satellite to be evaluated to a unified time grid to obtain a network phase sequence, and constructing a discrete frequency sample sequence set and an available frequency sample index set based on the network phase sequence include: A unified time grid is constructed using a preset reference sampling interval; The sparse and irregularly distributed clock difference sequence of the satellite to be evaluated is mapped onto the unified time grid to obtain the network phase sequence. Network points without observation in the unified time grid are marked as missing measurements. Traverse all adjacent grid points in the network phase sequence. When both adjacent grid points have observations, construct discrete frequency samples based on the phase difference between the adjacent grid points to obtain a set of discrete frequency sample sequences. Record the grid point location indices of all constructed discrete frequency samples as a set of available frequency sample indices.

4. The method for evaluating the stability of a spaceborne clock for sparse and irregular observations according to claim 3, characterized in that, The step of calculating the uncorrected Allan variance estimate under missing data conditions based on the discrete frequency sample sequence set and the available frequency sample index set, for each average time scale, by taking the intersection of the forward and backward windows with the available frequency sample index set at each center index, includes: For any center index, define the intersection of the forward window and the backward window on the set of available frequency sample indices; When both the forward window and the backward window are not empty, calculate the mean of the discrete frequency samples within the corresponding window respectively; A three-point difference value is constructed based on the mean of the discrete frequency samples within the window; All eligible central indices are counted to form a central index set, and the number of central index sets is counted. The uncorrected Allan variance estimate is calculated based on the three-point difference value and the number of central index sets.

5. The method for evaluating the stability of a spaceborne clock for sparse and irregular observations according to claim 1, characterized in that, The hybrid noise model determined by the network phase sequence includes at least two of white phase modulation noise, white frequency modulation noise, and random walk frequency modulation noise; The process of determining the mixed noise model from the network phase sequence is as follows: Based on the network phase sequence, a full ergodic three-point difference calculation is performed on the average factor corresponding to all average time scales to obtain a dense scatter dataset. Logarithmically bin the dense scatter dataset, and take a weighted average of the three-point difference calculation results within each bin to obtain a representative point set; Robust fitting is performed on the representative point set to obtain the fitting coefficients for white phase modulation noise, white frequency modulation noise and random walk frequency modulation noise respectively. Based on the fitting coefficients, the contribution values ​​of white phase modulation noise, white frequency modulation noise, and random walk frequency modulation noise at each average time scale are calculated, and the contribution values ​​are normalized to obtain the mixed noise weights, thereby determining the mixed noise model.

6. The method for evaluating the stability of a spaceborne clock for sparse and irregular observations according to claim 5, characterized in that, The process of calculating the mixed geometry bias correction factor based on the missing geometry of the available frequency sample index set and the mixed noise model determined by the network phase sequence is as follows: The missing geometry of the available frequency sample index set is fixed; After obtaining the mixed noise weights, the mixed geometric deviation correction factor is calculated using analytical formulas or Monte Carlo simulation.

7. The method for evaluating the stability of a spaceborne clock for sparse and irregular observations according to claim 1, characterized in that, The process of calculating a mixed correction factor using the mixed geometric deviation correction factor, correcting the uncorrected Allan variance estimate using the mixed correction factor, and obtaining the corrected Allan variance as the result of the onboard clock stability assessment specifically includes: The mixed correction factor is calculated using the aforementioned mixed geometric deviation correction factor; Multiply the uncorrected Allan variance estimate by the mixed correction factor to obtain the corrected Allan variance; The corrected Allan variance is output as the satellite clock stability evaluation result.

8. A system for evaluating the stability of a spaceborne clock for sparse and irregular observations, characterized in that, A method for evaluating the stability of a spaceborne clock for sparse and irregular observations, as described in any one of claims 1-7, includes: The ground operation and control system includes a ground operation and control center and at least one ground station, which is used for link planning, command issuance and observation data aggregation; The satellite to be evaluated carries an onboard clock, which is used to establish links with ground stations and observation satellites and to perform measurements. An observation satellite is used to establish an inter-satellite link with the satellite to be evaluated and to perform measurements. The data processing and evaluation module, deployed at the ground control center or the satellite to be evaluated, includes: The data acquisition module is used to acquire the sparse and irregularly distributed clock difference sequence of the satellite to be evaluated; The gridding and frequency construction module is used to map the sparse and irregularly distributed clock difference sequence of the satellite to be evaluated to a unified time grid to obtain a network phase sequence, and construct a discrete frequency sample sequence set and an available frequency sample index set based on the network phase sequence. The missing Allan variance estimation module is used to calculate the uncorrected Allan variance estimate under missing conditions based on the discrete frequency sample sequence set and the available frequency sample index set for each average time scale by taking the intersection of the forward window and the backward window with the available frequency sample index set at each center index. The correction factor calculation module is used to calculate the mixed geometry deviation correction factor based on the missing geometry of the available frequency sample index set and the mixed noise model determined by the network phase sequence. The correction module is used to calculate the mixed correction factor using the mixed geometric deviation correction factor, and then correct the uncorrected Allan variance estimate using the mixed correction factor to obtain the corrected Allan variance, which is used as the evaluation result of the onboard clock stability.

9. A computer device, characterized in that, include: Processor and computer-readable storage media; A processor, adapted to execute computer programs; A computer-readable storage medium storing a computer program, which, when executed by the processor, implements a method for evaluating the stability of a satellite clock for sparse and irregular observations as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program adapted to be loaded by a processor and executed as described in any one of claims 1-7, which is a method for evaluating the stability of a satellite clock for sparse and irregular observations.

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