A method for compensating for satellite clock error day boundary jumps based on epoch difference

Abstract

The application relates to a satellite clock error day boundary jump compensation method based on epoch difference, which comprises the following steps: step 1, analyzing main error items of satellite clock error day boundary jump, wherein the main error items include time reference deviation TDB and initial clock deviation ICB; step 2, on the basis of fully considering the time reference deviation TDB and the initial clock deviation ICB, combining data quality and model strength of the satellite clock error, and on the basis of the traditional satellite clock error day boundary jump compensation method based on single epoch, satellite clock error day boundary jump compensation item estimation and compensation are carried out. The method fully utilizes satellite clock error data of all epochs before and after the day boundary jump, accurately estimates the day boundary jump compensation item through average epoch difference minute difference data, and bridges the satellite clock error before and after the day boundary jump. The method can accurately compensate the satellite clock error day boundary jump, is beneficial to improving the continuity of the satellite clock error product, and improves the positioning accuracy at the day boundary.

Description

Technical Field

[0001] This invention relates to the field of high-precision positioning technology for satellite navigation receivers, specifically to a satellite clock difference daily boundary jump compensation method based on inter-epoch difference. Background Technology

[0002] First, satellite clock bias is the foundation of Precise Point Positioning (PPP). Currently, several International GNSS Service (IGS) analysis centers provide satellite clock bias products, including: the Center for Orbit Determination in Europe (CODE) in Switzerland, Natural Resources Canada (EMR), the European Space Agency (ESA), the GeoForschungs Zentrum (GFZ) in Germany, the Groupe de Rechercheen Geodesie Spatiale (GRG) in France, Jet Propulsion Labs (JPL) in the United States, the Massachusetts Institute of Technology (MIT) in the United States, the National Oceanic and Atmospheric Administration (NGS) in the United States, and the Scripps Institute of Oceanography (SIO) in the United States.

[0003] Secondly, users requiring cross-day data processing, such as those involved in clock bias product reprocessing, geological exploration, and island and reef mapping, have placed higher demands on the continuity of satellite clock bias products. Analysis centers typically employ batch processing least squares estimation strategies for satellite clock bias products provided on a daily basis, leading to nanosecond-level clock jumps at the day boundary—a phenomenon known as satellite clock bias day boundary jumps. Combining the components of satellite clock bias error terms, Time Scale Difference Biases (TDBs) and Initial Clock Biases (ICBs) are the main error terms causing satellite clock bias day boundary jumps. TDBs with an accuracy better than 10⁻⁶ seconds are absorbed by the receiver clock bias during PPP solution, not affecting the PPP positioning results, but impacting clock bias continuity at the day boundary. ICBs are absorbed by ambiguity parameters during PPP solution, affecting only pseudorange observations but not carrier phase observations, causing PPP positioning error fluctuations or even reconvergence.

[0004] Third, regarding the diurnal boundary jump in the final product of satellite clock bias across multiple days, continuous satellite clock bias can be estimated by jointly solving multi-day observation data. The literature also proposes using ambiguity superposition to reduce the independence of data between days, but this is limited by the calculation arc length not exceeding 8 days. Under the premise of directly using satellite clock bias products from various analysis centers, combining broadcast ephemeris to bridge the diurnal boundary jump of satellite clock bias can effectively compensate for the diurnal boundary jump caused by TDB. However, due to the limited accuracy of broadcast ephemeris clock bias, ICB is difficult to accurately compensate. Based on a full consideration of both TDB and ICB, the literature extrapolates the clock bias of the next epoch using the satellite clock bias of the first day, combines it with the satellite clock bias of the first epoch of the second day to estimate the diurnal boundary jump compensation term, and bridges the satellite clock bias before and after the diurnal boundary jump. This method fully considers the main error terms of the diurnal boundary jump of satellite clock bias through clock bias extrapolation, but estimating the diurnal boundary compensation term using only single-epoch satellite clock bias may introduce clock bias gross errors, resulting in low accuracy of diurnal boundary jump compensation.

[0005] Fourth, the aforementioned scholars' research mostly focuses on how to compensate for the daily boundary jump of satellite clock bias, with relatively little research on improving the estimation accuracy of the daily boundary jump compensation term. Therefore, studying and analyzing the main error terms of the daily boundary jump in satellite clock bias products, accurately estimating the daily boundary jump compensation term, and improving the compensation accuracy of traditional single-epoch (SE) based satellite clock bias daily boundary jump compensation methods are of great significance for improving the accuracy of cross-sky PPP positioning and the continuity of satellite clock bias products. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and propose a satellite clock difference day boundary jump compensation method based on interepoch difference.

[0007] The above-mentioned objective of this invention is achieved through the following technical solution: A satellite clock difference day boundary jump compensation method based on inter-epoch difference includes the following steps: Step 1: Analyze the main error terms of satellite clock bias day boundary jump. The main error terms include: time base deviation (TDB) and initial clock bias deviation (ICB). Step 2: Taking into full account the time base deviation (TDB) and initial clock bias (ICB), and combining the data quality and model strength of satellite clock bias, the satellite clock bias daily boundary jump compensation term is estimated and compensated based on the traditional single-epoch satellite clock bias daily boundary jump compensation method.

[0008] Moreover, step 1 includes: Step 1.1: Establish a mathematical model for satellite clock bias. The model formula is as follows: In the formula, aIndicates the analysis center, s Indicates satellite, Indicates satellite clock bias, Indicates TDB, Indicates ICB, This represents the theoretical value of satellite clock bias. Represents the satellite clock noise term; Step 1.2: Analyze the characteristics of the two errors. The time base deviation (TDB) can be eliminated when performing inter-satellite differences; the initial clock bias (ICB) can be eliminated when performing inter-epoch differences. Step 1.3: Combining the error characteristics of the time base deviation (TDB) and the initial clock bias (ICB), perform inter-satellite-to-epoch differential processing on the satellite clock bias of adjacent two epochs.

[0009] Furthermore, in step 1.3, the difference processing expression is as follows: In the formula, This represents the interstellar-epoch difference operator. Indicates the first and the Inter-satellite differential analysis was performed using the satellite clock bias data of the two satellites. Indicates the first and the The satellite clock difference data from two epochs are used to perform inter-epoch difference analysis.

[0010] Furthermore, step 2 includes: Step 2.1: Set the daily sequence expression for satellite clock bias, based on clock bias data with a 5-minute sampling interval, ignore short-term clock drift, and assume that the clock bias changes of adjacent epochs are approximately equal; Step 2.2: Construct the epoch difference sequence of satellite clock difference at non-solar boundaries and the epoch difference sequence of satellite clock difference at the solar boundary; Step 2.3: Take the mean of the differences between all epochs of two days as the estimator of the daily boundary difference; Step 2.4: Use the median method to detect and eliminate outliers in clock error; calculate the estimated value of the daily boundary jump compensation term by subtracting the mean difference estimate from the difference of the last epoch of the last day. Step 2.5 Use the estimated value of the compensation term obtained by solving to bridge and correct the satellite clock error sequence before the solar boundary, so as to obtain a continuous and smooth compensated satellite clock error sequence.

[0011] Moreover, in step 2.1, the first k The satellite clock bias data sequence for each day is represented as follows: In the formula, Indicates satellite s No.k Heavenly i Chronological clock difference data sequence.

[0012] Furthermore, in step 2.2, the difference sequence between satellite clock epochs at non-solar boundaries is represented as follows: In the formula, This represents the parameter indicating the linear variation of satellite clock bias at non-solar boundaries. This indicates the sampling interval of the satellite clock bias data sequence; without atomic clock switching or frequency jumps, the first... k Tianhe Di k +1 day They are approximately equal; The difference sequence of satellite clock errors between epochs at the solar boundary is represented as follows: In the formula, Indicates the first k The last calendar year of the heavens, Indicates the first k The first epoch of +1 day, This represents the parameter indicating the linear variation of satellite clock error at the solar boundary.

[0013] Furthermore, in step 2.3, the expression for the inter-epoch difference estimate of satellite clock bias at the solar boundary is: In the formula, M Indicates the first k Total number of epochs in the Tianwei clock bias data sequence N Indicates the first k Total number of epochs in the +1 day satellite clock bias data sequence This represents the difference operator between epochs. This represents the epochal difference estimate of satellite clock difference at the solar boundary.

[0014] Furthermore, the estimator of the daily boundary jump compensation term in step 2.4 is expressed as follows: .

[0015] Moreover, in step 2.5, the first k The satellite clock bias data sequence after the overpass connection can be represented as: .

[0016] Advantages and positive effects of this invention 1. This invention starts from the error mechanism and takes into account the two core error terms, Time Base Deviation (TDB) and Initial Clock Deviation (ICB). It eliminates TDB by inter-satellite difference and ICB by inter-epoch difference. It clarifies the error propagation law through inter-satellite-epoch joint difference. The theoretical basis is rigorous and complete, and it can suppress satellite clock deviation day boundary jumps from the root.

[0017] 2. This invention abandons the traditional method of estimating compensation terms based solely on single-epoch data. Instead, it fully utilizes satellite clock difference data from all epochs before and after the day boundary and uses the mean of the differences between epochs as the day boundary difference estimator. This effectively avoids the estimation bias caused by gross errors in single-epoch clock differences and significantly improves the estimation accuracy and robustness of the day boundary jump compensation term.

[0018] 3. This invention introduces the median method to detect and eliminate gross clock errors, blocking the interference of gross errors on the calculation of compensation parameters and further ensuring the reliability of the compensation results. At the same time, it reasonably ignores small higher-order clock drifts, sets the clock error changes of adjacent epochs to be approximately equal, and sets the parameters of trans-linear changes of the antenna to be consistent when there is no atomic clock jump. The model is simplified and reasonable, and fits the actual characteristics of satellite clock error changes.

[0019] 4. This invention bridges and corrects the cross-sky satellite clock difference sequence by solving the day boundary jump compensation term, which can obtain continuous and smooth satellite clock difference time series data, significantly improving the cross-sky continuity of satellite clock difference products; it can improve the accuracy fluctuation problem of cross-sky precise single-point positioning, avoid positioning re-convergence, and meet the cross-sky high-precision positioning application needs such as clock difference product reprocessing, geological exploration, and island and reef mapping.

[0020] In summary, compared with the traditional single-epoch compensation method, the method proposed in this invention makes full use of satellite clock error data of all epochs before and after the day boundary jump. By calculating the mean of the difference between the two days' satellite clock error epochs, the satellite clock error day boundary jump compensation term is estimated, and then the satellite clock error day boundary jump is bridged. This can effectively avoid the gross errors in the first epoch satellite clock error data in the traditional single-epoch compensation method, which is conducive to improving the continuity of satellite clock error products and improving the positioning accuracy at the day boundary. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the satellite clock difference day boundary jump compensation method based on interepoch difference of the present invention. Detailed Implementation

[0022] The present invention will be further described in detail below with reference to specific embodiments.

[0023] For a satellite clock difference day boundary jump compensation method based on inter-epoch difference, please refer to [link / reference]. Figure 1 The core idea of ​​this invention is: First, the error characteristics and propagation laws of the time base deviation (TDB) and initial clock bias deviation (ICB) of satellite clock bias daily boundary jumps are analyzed. Among these, TDB and ICB are the core error terms of satellite clock bias daily boundary jumps. Then, based on the traditional single-epoch compensation method, inter-epoch and inter-satellite differences are introduced. The average of multi-day, multi-epoch differences is used to replace the single-epoch estimate. Combined with gross error elimination, the daily boundary jump compensation term is accurately estimated, achieving smooth bridging of satellite clock bias daily boundaries and improving compensation accuracy, clock bias continuity, and cross-sky PPP positioning performance. Specifically, the following steps are included: Step 1: Analyze the main error terms of satellite clock bias day boundary jump, including the following steps: Step 1.1: Based on the equivalence of three satellite clock bias estimation methods—non-difference, inter-epoch difference, and hybrid difference—a satellite clock bias mathematical model is established. The mathematical model consists of TDB, ICB, theoretical clock bias values, and a noise term. The model formula is as follows: In the formula, a Indicates the analysis center, s Indicates satellite, Indicates satellite clock bias, Indicates TDB, Indicates ICB, This represents the theoretical value of satellite clock bias. This represents the satellite clock noise term.

[0024] Step 1.2: Analyze the characteristics of the two error effects: TDB: Caused by different selection strategies for the reference clock in different day clock difference estimations, with an accuracy better than 10. -6 Under the premise of s, the PPP solution is absorbed by the receiver clock bias, which does not affect the PPP positioning result, and the inter-satellite differential can eliminate it; ICB: is the bias introduced into the initial satellite clock bias during clock bias estimation. The satellite-related ICB is absorbed by the ambiguity parameter during PPP solution, affecting only the pseudorange observations and not the carrier phase observations, causing fluctuations in PPP positioning error or even reconvergence. Interepoch difference can eliminate it. Step 1.3: To analyze the relationship between the daily boundary jump of satellite clock bias and the various error terms in the mathematical model of satellite clock bias, and combining the error characteristics of TDB and ICB, inter-satellite-to-epoch difference processing is performed on the satellite clock bias of adjacent two epochs. The difference processing expression is as follows: In the formula, This represents the interstellar-epoch difference operator. Indicates the first and the Inter-satellite differential analysis was performed using the satellite clock bias data of the two satellites. Indicates the first and the Satellite clock bias data from two epochs are differentially analyzed between epochs; TDB, which is independent of the satellite, is eliminated during inter-satellite differential analysis, while ICB is constant within the continuous clock bias solution arc and is eliminated during inter-epoch differential analysis.

[0025] Step 2: Taking into full account both TDB and ICB, and considering the data quality and model strength of satellite clock bias, the satellite clock bias daily boundary jump compensation term is estimated and compensated based on the traditional single-epoch satellite clock bias daily boundary jump compensation method. This includes the following steps: Step 2.1: Define the daily sequence expression for satellite clock bias; use satellite clock bias data with a 5-minute sampling interval as the fitting data. Since the clock drift parameter of the quadratic polynomial model is on the order of 10... -26 In short-term satellite clock bias forecasting, the clock bias can be ignored, and the clock bias changes between adjacent epochs are assumed to be approximately equal; among them, the 1st... k The satellite clock bias data sequence for each day is represented as follows: In the formula, Indicates satellite s No. k Heavenly i Chronological clock difference data sequence.

[0026] Step 2.2, for the first k At the boundary between the solar and non-solar celestial spheres, satellite clock differences are analyzed between epochs to eliminate the epoch. k The ICB of the satellite clock difference data sequence; then the difference sequence between satellite clock difference epochs at non-solar boundaries is expressed as: In the formula, This represents the parameter indicating the linear variation of satellite clock bias at non-solar boundaries. This indicates the sampling interval of the satellite clock bias data sequence; without atomic clock switching or frequency jumps, the first... k Tianhe Di k +1 day They are approximately equal; The difference sequence of satellite clock errors between epochs at the solar boundary is represented as follows: In the formula, Indicates the first k The last calendar year of the heavens, Indicates the first k The first epoch of +1 day, This represents the parameter indicating the linear variation of satellite clock error at the solar boundary.

[0027] Step 2.3: To reduce the fitting error of the clock difference model and avoid gross errors in single-epoch clock differences, the first... k and k The mean of the epoch differences of the satellite clock bias over all epochs in the +1-day period is used as the epoch difference estimate of the satellite clock bias at the day boundary. Its expression is as follows: In the formula, M Indicates the first k Total number of epochs in the Tianwei clock bias data sequence N Indicates the first k Total number of epochs in the +1 day satellite clock bias data sequence This represents the difference operator between epochs. This represents the epochal difference estimate of satellite clock difference at the solar boundary.

[0028] Step 2.4: Use the median method to detect and eliminate clock errors; calculate the daily boundary jump compensation term by subtracting the mean difference estimate from the difference at the last epoch of the last day. Using the median method to detect the first k The clock bias outliers of the day are removed, and the inter-epoch difference estimators of satellite clock bias are combined with the epoch-level clock bias gross errors. k By subtracting the satellite clock difference values ​​between the last two epochs of the day, the estimate of the daily boundary jump compensation term is obtained, and its expression is as follows: Step 2.5: Using the estimated value of the solved compensation term, bridge and correct the satellite clock error sequence before the day boundary. k The satellite clock bias data sequence after the overpass connection can be represented as: .

[0029] Although embodiments and drawings of the present invention have been disclosed for illustrative purposes, those skilled in the art will understand that various substitutions, variations and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the scope of the present invention is not limited to the contents disclosed in the embodiments and drawings.

Claims

1. A satellite clock difference day boundary jump compensation method based on inter-epoch difference, characterized in that: Includes the following steps: Step 1: Analyze the main error terms of satellite clock bias day boundary jump. The main error terms include: time base deviation (TDB) and initial clock bias deviation (ICB). Step 2: Taking into full account the time base deviation (TDB) and initial clock bias (ICB), and combining the data quality and model strength of satellite clock bias, the satellite clock bias daily boundary jump compensation term is estimated and compensated based on the traditional single-epoch satellite clock bias daily boundary jump compensation method.

2. The satellite clock difference daily boundary jump compensation method based on inter-epoch difference according to claim 1, characterized in that: Step 1 includes: Step 1.1: Establish a mathematical model for satellite clock bias. The model formula is as follows: ； In the formula, a Indicates the analysis center, s Indicates satellite, Indicates satellite clock bias, Indicates TDB, Indicates ICB, This represents the theoretical value of satellite clock bias. Represents the satellite clock noise term; Step 1.2: Analyze the characteristics of the two errors. The time base deviation (TDB) can be eliminated when performing inter-satellite differences; the initial clock bias (ICB) can be eliminated when performing inter-epoch differences. Step 1.3: Combining the error characteristics of the time base deviation (TDB) and the initial clock bias (ICB), perform inter-satellite-to-epoch differential processing on the satellite clock bias of adjacent two epochs.

3. The satellite clock difference daily boundary jump compensation method based on inter-epoch difference according to claim 2, characterized in that: In step 1.3, the difference processing expression is as follows: ； In the formula, This represents the interstellar-epoch difference operator. Indicates the first and the Inter-satellite differential analysis was performed using the satellite clock bias data of the two satellites. Indicates the first and the The satellite clock difference data from two epochs are used to perform inter-epoch difference analysis.

4. The satellite clock difference day boundary jump compensation method based on inter-epoch difference according to claim 1, characterized in that: Step 2 includes: Step 2.1: Set the daily sequence expression for satellite clock bias, based on clock bias data with a 5-minute sampling interval, ignore short-term clock drift, and assume that the clock bias changes of adjacent epochs are approximately equal; Step 2.2: Construct the epoch difference sequence of satellite clock difference at non-solar boundaries and the epoch difference sequence of satellite clock difference at the solar boundary; Step 2.3: Take the mean of the differences between all epochs of two days as the estimator of the daily boundary difference; Step 2.4: Use the median method to detect and eliminate outliers in clock error; calculate the estimated value of the daily boundary jump compensation term by subtracting the mean difference estimate from the difference of the last epoch of the last day. Step 2.5 Use the estimated value of the compensation term obtained by solving to bridge and correct the satellite clock error sequence before the solar boundary, so as to obtain a continuous and smooth compensated satellite clock error sequence.

5. The satellite clock difference daily boundary jump compensation method based on inter-epoch difference according to claim 4, characterized in that: In step 2.1, the first k The satellite clock bias data sequence for each day is represented as follows: ； In the formula, Indicates satellite s No. k Heavenly i Chronological clock difference data sequence.

6. The satellite clock difference daily boundary jump compensation method based on inter-epoch difference according to claim 5, characterized in that: In step 2.2, the difference sequence between satellite clock epochs at non-solar boundaries is represented as follows: ； In the formula, This represents the parameter indicating the linear variation of satellite clock bias at non-solar boundaries. This indicates the sampling interval of the satellite clock bias data sequence; without atomic clock switching or frequency jumps, the first... k Tianhe Di k +1 day They are approximately equal; The difference sequence of satellite clock errors between epochs at the solar boundary is represented as follows: ； In the formula, Indicates the first k The last calendar year of the heavens, Indicates the first k The first epoch of +1 day, This represents the parameter indicating the linear variation of satellite clock error at the solar boundary.

7. The satellite clock difference day boundary jump compensation method based on inter-epoch difference according to claim 6, characterized in that: In step 2.3, the expression for the inter-epoch difference estimate of satellite clock error at the solar boundary is: ； In the formula, M Indicates the first k Total number of epochs in the Tianwei clock bias data sequence N Indicates the first k Total number of epochs in the +1 day satellite clock bias data sequence This represents the difference operator between epochs. This represents the epochal difference estimate of satellite clock difference at the solar boundary.

8. The satellite clock difference day boundary jump compensation method based on inter-epoch difference according to claim 7, characterized in that: In step 2.4, the estimator of the daily boundary jump compensation term is expressed as follows: 。 9. The satellite clock difference daily boundary jump compensation method based on inter-epoch difference according to claim 8, characterized in that: In step 2.5, the first k The satellite clock bias data sequence after the overpass connection can be represented as: 。

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