An ionospheric oblique total electron content extraction precision evaluation method and system based on co-location station inter-difference

Abstract

The application discloses a kind of ionospheric oblique total electron content extraction precision evaluation method and system based on co-sited inter-station single difference, and the observation statistical unit based on single ephemeris is improved observation precision.Two co-sited receivers configured and using the same satellite navigation system are used to obtain the oblique total electron content observation values of the same batch of common visible satellites, the inter-station single difference sequence is processed in ephemeris, the cross-star common component of the common hardware bias difference value is eliminated, the receiver end common hardware bias term does not participate in the dispersion statistics in ephemeris, and the influence of receiver hardware bias drift, step change and trend term on the precision evaluation result is reduced.In a preset time window, each valid ephemeris is weighted and combined according to ephemeris weight, and the combined standard deviation is used as the oblique total electron content extraction precision evaluation result corresponding to the preset time window, to improve the time resolution, stability and reliability of the oblique total electron content extraction precision evaluation.

Description

Technical Field

[0001] This invention relates to the field of global satellite navigation and positioning and space physics exploration, and in particular to a method and system for evaluating the accuracy of ionospheric oblique total electron content extraction based on single difference between co-located stations. Background Technology

[0002] Existing co-located receiver experiments utilize inter-station single differences to weaken or eliminate satellite-end differential code bias, orbital error, clock bias, and common atmospheric propagation terms, and evaluate the accuracy of oblique total electron content (STEC) extraction based on the dispersion of inter-station single differences. However, traditional evaluation methods typically statistically analyze the peak-to-peak value or dispersion of the single-difference sequence over a full-day scale, assuming that the receiver differential code bias (RDCB) remains stable within a statistical period and that the daily-scale single-difference results approximately follow a normal distribution. In actual observations, RDCB can be affected by factors such as receiver hardware status, temperature changes, equipment restarts, or firmware updates, resulting in hourly drift or abrupt changes. The single-difference sequence may also contain trend terms caused by multipath, arc-smoothing errors, or changes in receiver hardware. In such cases, traditional long-term statistics may be primarily determined by trend terms or hardware bias changes, rather than by the oblique total electron content (STEC) extraction error itself, thus deviating from the fundamental idea of ​​co-located experiments to characterize extraction accuracy through single-difference dispersion.

[0003] A new method for evaluating the accuracy of oblique total electron content extraction is needed to solve the above-mentioned technical problems. Summary of the Invention

[0004] The purpose of this invention is to provide a method for evaluating the accuracy of ionospheric oblique total electron content extraction based on single difference between co-located stations, in order to solve the technical problem of inaccurate accuracy evaluation results in the prior art.

[0005] The present invention also aims to provide an evaluation system for evaluating the accuracy of ionospheric oblique total electron content extraction using a method based on single difference between co-located stations.

[0006] The technical solution of this invention to solve its technical problem is as follows:

[0007] A method for evaluating the accuracy of ionospheric oblique total electron content extraction based on single difference between co-located stations, specifically including the following steps:

[0008] S1: Obtain the oblique total electron content observation values ​​of two co-located receivers using the same satellite navigation system within the same epoch for the same batch of common visible satellites under the same signal or frequency conditions;

[0009] S2: By sequentially calculating the inter-station single difference value for each commonly visible satellite in the same batch within the same epoch of two satellite navigation system receivers, the inter-station single difference value of each commonly visible satellite in the same batch is obtained. The inter-station single difference values ​​of the same batch constitute the inter-station single difference sequence of the commonly visible satellites in the same batch within one epoch.

[0010] S3: Calculate the mean of the inter-station single difference sequence for the same batch of commonly visible satellites within an epoch; use the mean of the inter-station single difference sequence to perform intra-epoch centering processing on the inter-station single difference sequence to eliminate the cross-satellite common component of the common hardware deviation difference and obtain the single difference residual sequence; calculate the intra-epoch variance and intra-epoch standard deviation of the inter-station single difference based on the single difference residual sequence; use the intra-epoch variance of the inter-station single difference as a cross-satellite dispersion statistic of the difference between the non-common errors extracted by the oblique total electron content of two receivers within an epoch;

[0011] S4: Based on the variance within the single epoch of the inter-station difference and the error propagation relationship, the cross-satellite dispersion of the difference between the non-common errors of the oblique total electron content extraction of the two receivers is mapped to the equivalent single-station oblique total electron content extraction non-common error, and the equivalent single-station oblique total electron content extraction variance and the equivalent single-station oblique total electron content extraction standard deviation are calculated.

[0012] S5: Within a preset time window, the variance of the equivalent single-station oblique total electron content extraction for each effective epoch is weighted and merged according to the epoch weight to obtain the merged variance. The merged standard deviation is then calculated based on the merged variance, and the merged standard deviation is used as the evaluation result of the oblique total electron content extraction accuracy for the preset time window.

[0013] Preferably, the oblique total electron content observation value in step S1 is obtained by processing the satellite's dual-frequency pseudorange observation value and dual-frequency carrier phase observation value through an oblique total electron content extraction method; the oblique total electron content extraction method includes carrier phase smoothing pseudorange method, non-differential non-combined precise single-point positioning floating-point solution method or non-differential non-combined precise single-point positioning fixed solution method.

[0014] Preferably, the specific formulas for the mean of the single-difference sequence, the single-difference residual, the variance within epochs of the inter-station single-difference sequence, and the standard deviation within epochs of the inter-station single-difference sequence in step S3 are as follows:

[0015] ;

[0016] ;

[0017] ;

[0018] ;

[0019] in, Let represent the mean of the inter-station single-difference sequence of the same batch of commonly visible satellites within the t-th epoch, where t represents the epoch number. This represents the number of commonly visible satellites within the t-th epoch, where j represents the index of the commonly visible satellite. This represents the inter-station single difference value of the j-th commonly visible satellite within the t-th epoch. Indicates the first Within an epoch, the first Single-difference residuals of three commonly visible satellites This represents the inter-station single difference within the epth epth . Indicates the first The station-to-station single difference and standard deviation within an epoch are calculated within one epoch; the above calculation process is completed within one epoch.

[0020] Preferably, the specific formulas for calculating the variance and standard deviation of the equivalent single-station oblique total electron content extraction in step S4 are as follows:

[0021] ;

[0022] ;

[0023] in, This represents the variance extracted from the equivalent single-station oblique total electron content within the t-th epoch. This represents the standard deviation of the single difference within the t-th epoch. This represents the standard deviation of the equivalent single-station oblique total electron content extracted within the t-th epoch.

[0024] Preferably, the preset time window in step S5 is specifically an hourly window, a daily window, a monthly window, or a custom time window corresponding to a specific spatial weather event.

[0025] Preferably, the epoch weight in step S5 is determined based on the number of effective common visible satellites in each epoch, or the common visible satellite elevation angle statistics, or the carrier-to-noise ratio statistics, or the single-difference residual statistics.

[0026] Preferably, when the epoch weight is the weight of the number of effective commonly visible satellites, the specific formulas for the combined variance and the combined standard deviation are as follows:

[0027] ;

[0028] ;

[0029] ;

[0030] Where T represents the set of valid epochs within the preset time window, Indicates the first Each epoch corresponds to an epoch weight. Indicates the first The number of effectively co-visible satellites within a given epoch. Indicates the first Variance extraction of the equivalent single-station oblique total electron content corresponding to each epoch. Indicates the combined variance. This represents the combined standard deviation.

[0031] Preferred options also include:

[0032] S6: Obtain the space weather index corresponding to each epoch, determine the geomagnetic quiet time window and the geomagnetic disturbance time window based on the space weather index, and obtain the corresponding merged standard deviation. Calculate the oblique total electron content extraction accuracy degradation rate based on the merged standard deviation corresponding to the geomagnetic quiet time window and the geomagnetic disturbance time window.

[0033] Preferably, step S5 further includes: generating an ionospheric observation quality evaluation index based on the merged standard deviation.

[0034] An evaluation system for assessing the accuracy of ionospheric oblique total electron content extraction using a method based on single-difference between co-located stations includes:

[0035] The data acquisition module is used to acquire the oblique total electron content observation values ​​of two co-located receivers using the same satellite navigation system within the same epoch for the same batch of common visible satellites under the same signal or frequency conditions.

[0036] The inter-station single difference construction module is used to calculate the inter-station single difference value for each commonly visible satellite in the same batch within the same epoch of two satellite navigation system receivers in turn, thereby obtaining the inter-station single difference value for each commonly visible satellite in the same batch. The inter-station single difference values ​​in the same batch constitute the inter-station single difference sequence of the commonly visible satellites in the same batch within one epoch.

[0037] The epoch-by-epoch variance statistics module is used to calculate the mean of the inter-station single difference sequence for the same batch of commonly visible satellites within an epoch. The mean of the inter-station single difference sequence is used to perform intra-epoch centering processing on the inter-station single difference sequence to eliminate the cross-satellite common component of the common hardware deviation difference and obtain the single difference residual sequence. Based on the single difference residual sequence, the intra-epoch variance and intra-epoch standard deviation of the inter-station single difference are calculated. The intra-epoch variance of the inter-station single difference is used as a cross-satellite dispersion statistic of the difference between the non-common error of the oblique total electron content extraction of two receivers within an epoch.

[0038] The single-station accuracy mapping module is used to map the cross-satellite dispersion of the difference between the non-common errors of the oblique total electron content extraction of two receivers to the equivalent single-station oblique total electron content extraction non-common error based on the variance within the single epoch of the inter-station single difference and the error propagation relationship, and to calculate the equivalent single-station oblique total electron content extraction variance and the equivalent single-station oblique total electron content extraction standard deviation.

[0039] The time window merging module is used to perform weighted merging of the variance of the equivalent single-station oblique total electron content extraction for each effective epoch within a preset time window, according to the epoch weight, to obtain the merged variance, and calculate the merged standard deviation based on the merged variance, and use the merged standard deviation as the evaluation result of the oblique total electron content extraction accuracy corresponding to the preset time window.

[0040] The beneficial effects of this invention are as follows: It improves observation accuracy by using a single epoch-based observation statistical unit. It acquires the oblique total electron content observations of two co-located receivers using the same satellite navigation system within the same epoch for the same batch of commonly visible satellites under the same signal or frequency conditions. The inter-station single difference values ​​are calculated using these oblique total electron content observations, resulting in an inter-station single difference sequence. The inter-station single difference sequence is then centered within an epoch to eliminate the cross-satellite common component of the common hardware bias difference and obtain a single difference residual sequence. This ensures that the common hardware bias term at the receiver end does not participate in the intra-epoch dispersion statistics, reducing the impact of receiver hardware bias drift, step changes, and trend terms on the accuracy evaluation results. This invention does not require the assumption that the diurnal-scale inter-station single difference approximately follows a normal distribution, nor does it require the assumption that the common hardware bias at the receiver end remains constant within the day. This avoids the evaluation distortion caused by traditional peak-to-peak conversion methods when the inter-station single difference exhibits multi-peak, skewed, long-tailed, or obvious trend characteristics. Based on the single-difference residual sequence, the inter-station intra-epoch variance is calculated. Then, according to the inter-station intra-epoch variance and error propagation relationship, the cross-satellite dispersion of the difference in non-common errors in oblique total electron content extraction from two receivers is mapped to the equivalent single-station non-common error in oblique total electron content extraction. The equivalent single-station oblique total electron content extraction variance and standard deviation are then calculated. Finally, within a preset time window, the equivalent single-station oblique total electron content extraction variances corresponding to each effective epoch are weighted and merged according to epoch weights to obtain the merged variance and merged standard deviation. The merged standard deviation is used as the oblique total electron content extraction accuracy evaluation result for the preset time window, improving the temporal resolution, stability, and reliability of the oblique total electron content extraction accuracy evaluation. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the overall process of the method of the present invention;

[0042] Figure 2These are the probability histograms, fitted normal probability density function curves, and standard normal QQ plots of the zero-baseline EIL3-EIL4 single-difference ionospheric observations in verification method 1 of this invention; CCL corresponding subplots (a) and (d), PPP floating-point solution corresponding subplots (b) and (e), and PPP fixed solution corresponding subplots (c) and (f).

[0043] Figure 3 The graphs are the probability histogram, fitted normal probability density function curve, and standard normal QQ plot of the short baseline STJ3-STJO single-difference ionospheric observations in the verification method 1 of this invention; CCL corresponding subplots (a) and (d), PPP floating-point solution corresponding subplots (b) and (e), and PPP fixed solution corresponding subplots (c) and (f).

[0044] Figure 4 These are the single-difference ionospheric observations of the short baseline ZIM2-ZIMM in DOY 118 (top row subplot) and DOY 99 (bottom row subplot) in 2024, as verified by Method 2 of this invention; CCL corresponds to subplots (a) and (d), PPP floating-point solutions correspond to subplots (b) and (e), and PPP fixed solutions correspond to subplots (c) and (f);

[0045] Figure 5 These are the single-difference ionospheric observations of the zero baseline GODZ-GODE (upper row subplot) and short baseline USN7-WDC5 (lower row subplot) for the year 001 of 2024 in the verification method 3 of this invention; CCL corresponds to subplots (a) and (d), PPP floating-point solution corresponds to subplots (b) and (e), and PPP fixed solution corresponds to subplots (c) and (f);

[0046] Figure 6 The epoch-level STEC extraction accuracy index (a) obtained by using PPP floating-point solution during the period from year 120 to 139 of EIL3 station in 2024 in verification method 3 of this invention, as well as the corresponding ROTI (b) and AATR (c);

[0047] Figure 7 The hourly STEC extraction accuracy index obtained by using PPP floating-point solution during the period from day 126 to 139 of 2024 in the verification method 3 of this invention; the zero baseline EIL3-EIL4 corresponds to sub-figure (a), and the short baselines YELL-YEL2, KIR0-KIR8 and STJ3-STJO correspond to sub-figures (b), (c) and (d) respectively. Detailed Implementation

[0048] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. In the prior art, co-located experimental configurations include two types:

[0049] 1. Zero Baseline: Two receivers are connected to the same antenna and low-noise amplifier (LNA) via an RF power divider. Common error terms such as atmospheric delay, orbit / clock error, and multipath reflection of satellite RF signals can be reduced or canceled out, and the residual only characterizes the receiver's internal background thermal noise and baseband processing deviation.

[0050] 2. Short Baseline: Two receivers are connected to their respective independent antennas, with the antenna spacing less than a preset threshold. Common atmospheric and satellite errors are canceled out, but the multipath effect of the local microenvironment is preserved. This is used to evaluate the receiver's accuracy in extracting the Comprehensive Oblique Total Electron Content (STEC) under real-world observation conditions.

[0051] The station information for all short baselines and zero baselines used in this method and the corresponding verification method are shown in Table 1.

[0052]

[0053] like Figure 1 As shown, this invention discloses a method for evaluating the accuracy of ionospheric oblique total electron content extraction based on single difference between co-located stations, specifically including the following steps:

[0054] S1: Obtain the oblique total electron content observation values ​​of two co-located receivers using the same satellite navigation system within the same epoch for the same batch of common visible satellites under the same signal or frequency conditions;

[0055] In practical applications, the observed values ​​can be preprocessed, specifically by performing data integrity checks, outlier removal, cycle slip detection and repair, observation arc segment division, and satellite elevation angle cutoff processing. The satellite elevation angle cutoff value is 15° to mitigate the adverse effects of low elevation angle observations caused by tropospheric mapping error amplification and environmental multipath influence. The oblique total electron content observation value in step S1 is obtained based on the satellite's dual-frequency pseudorange and dual-frequency carrier phase observation values ​​through oblique total electron content extraction methods. These methods include carrier phase smoothing pseudorange, non-differential non-combined precise single-point positioning floating-point solution, or non-differential non-combined precise single-point positioning fixed solution. Using the above oblique total electron content extraction algorithm can improve the performance of oblique total electron content (STEC) extraction under different algorithms, different station environments, and zero-baseline and short-baseline conditions within a unified framework.

[0056] During the acquisition of observations, precise orbit, precise clock bias, satellite uncalibrated phase delay product data, and space weather index data can also be acquired simultaneously as needed. Among these, precise orbit, precise clock bias, and satellite uncalibrated phase delay product data primarily serve the front-end extraction of total oblique electron content (STEC), while the space weather index primarily serves the classification and interpretation of the back-end evaluation results. Their roles differ. For example, when using the non-differential, non-combined precise single-point positioning floating-point solution method or the non-differential, non-combined precise single-point positioning (PPP) fixed solution method to extract STEC, precise orbit product data is used to provide accurate satellite position and correct orbital errors, while precise clock bias product data is used to correct satellite clock bias. In the non-differential, non-combined precise single-point positioning (PPP) fixed solution method, satellite uncalibrated phase delay product data is used to correct satellite-end phase deviation, restore the integer characteristics of ambiguity, and achieve ambiguity fixation. By affecting the solution quality of the STEC observations, it indirectly affects the subsequent inter-station single-difference variance and accuracy evaluation results, but does not directly participate in the statistical calculations of steps S3-S5. This allows the residual common error to be further reduced in the inter-station single difference when both receivers use the same precision products.

[0057] S2: By sequentially calculating the inter-station single difference value for each commonly visible satellite in the same batch within the same epoch of two satellite navigation system receivers, the inter-station single difference value of each commonly visible satellite in the same batch is obtained. The inter-station single difference values ​​of the same batch constitute the inter-station single difference sequence of the commonly visible satellites in the same batch within one epoch.

[0058] Let the first The receiver is at the Within each epoch, the first The oblique total electron content observation values ​​obtained from three common visible satellites are The observed value of the oblique total electron content is expressed as:

[0059] ;

[0060] in, Indicates the first Within an epoch, the first True values ​​of oblique total electron content corresponding to three common visible satellites; Indicates the first The receiver is at the Within each epoch, there is a receiver-side common hardware bias term that is approximately the same for all commonly visible satellites, and the common hardware bias term includes receiver differential code bias. This indicates the non-common error in the extraction of total electron content along the oblique direction.

[0061] The formula for calculating the single difference between stations is:

[0062] ;

[0063] ;

[0064] ;

[0065] in, and These represent the numbers representing receiver A and receiver B at the [number]th [year]. Within each epoch, for the first Oblique total electron content observations obtained from three common visible satellites; and These represent the numbers representing receiver A and receiver B at the [number]th [year]. Within each epoch, there is a receiver-side common hardware deviation term that is approximately the same for all commonly visible satellites; This indicates the difference in common hardware deviation between the two receivers; and These represent the non-common errors in the extraction of the total electron content at an oblique angle for receiver A and receiver B, respectively. This represents the difference in non-common error between the two receivers when extracting the total electron content at an angle.

[0066] Specific non-common errors in oblique total electron content extraction generally include: observation noise, receiver internal processing errors, processing errors of the oblique total electron content extraction method, and other non-common error components not canceled out by inter-station single differences. For short baseline configuration, non-common errors also include: incompletely canceled local multipath differences, antenna and feeder differences, and residual propagation path differences.

[0067] S3: Calculate the mean of the inter-station single-difference sequence for the same batch of commonly visible satellites within an epoch; use the mean of the inter-station single-difference sequence to perform intra-epoch centering processing on the inter-station single-difference sequence, eliminating the cross-satellite common component of the common hardware deviation difference and obtaining the single-difference residual sequence; calculate the intra-epoch variance and intra-epoch standard deviation of the inter-station single-difference sequence based on this single-difference residual sequence; use the intra-epoch variance of the inter-station single-difference sequence as a cross-satellite dispersion statistic of the difference between the non-common errors extracted from the oblique total electron content of two receivers within an epoch; the specific formulas for the mean of the single-difference sequence, the single-difference residual, the intra-epoch variance of the inter-station single-difference sequence, and the intra-epoch standard deviation of the inter-station single-difference sequence in step S3 are as follows:

[0068] ;

[0069] ;

[0070] ;

[0071] ;

[0072] in, Let represent the mean of the inter-station single-difference sequence of the same batch of commonly visible satellites within the t-th epoch, where t represents the epoch number. This represents the number of commonly visible satellites within the t-th epoch, where j represents the index of the commonly visible satellite. This represents the inter-station single difference value of the j-th commonly visible satellite within the t-th epoch. Indicates the first Within an epoch, the first Single-difference residuals of three commonly visible satellites This represents the inter-station single difference within the epth epth . Indicates the first The inter-station single difference and standard deviation within each epoch; the above calculation process is completed within one epoch, ensuring the data consistency of the receiver during the statistical period and improving the accuracy of the accuracy evaluation results.

[0073] Furthermore, the calculation formula for the single difference between stations in step S2 shows that:

[0074] ;

[0075] because Within the same epoch, for each commonly visible satellite, there are approximately the same additive common terms. The formula for the mean of the inter-station single-difference sequence in step S3 is further as follows:

[0076] ;

[0077] This represents the mean of the non-common error differences among the commonly visible satellites within this epoch.

[0078] In step S3, the inter-station single-difference sequence is centered within an epoch using the mean of the inter-station single-difference sequence to eliminate the cross-satellite common component of the common hardware deviation difference and obtain the single-difference residual sequence. The specific process is as follows:

[0079] ;

[0080] It is evident that the single-difference residual no longer contains This ensures that the difference in common hardware deviation between the two receivers does not affect the cross-satellite dispersion statistic of the difference in non-common error in the extraction of oblique total electron content between the two receivers within one epoch, thereby improving the accuracy of the single-station oblique total electron content extraction precision results.

[0081] Due to the inter-station single difference epoch internal variance obtained in step S3 Therefore, the calendar The variance of the cross-satellite dispersion, calculated by taking the set of effectively visible common satellites as the statistical object, is obtained by extracting the difference in non-common error of the oblique total electron content of two receivers within one epoch. Therefore, the variance within one epoch of this station's single difference is... It can be used as an estimate of two receivers within an epoch.

[0082] S4: Based on the variance within the single epoch of the inter-station difference and the error propagation relationship, the cross-satellite dispersion of the difference between the non-common errors of the oblique total electron content extraction of the two receivers is mapped to the equivalent single-station oblique total electron content extraction non-common error, and the equivalent single-station oblique total electron content extraction variance and the equivalent single-station oblique total electron content extraction standard deviation are calculated.

[0083] Since the non-common errors of the two receivers in extracting the total electron content at an angle are uncorrelated or their covariance is negligible, and given that the variances of the non-common errors of the two receivers are approximately equal, the variance of the difference between the non-common errors of the two receivers can be expressed as follows, based on the error propagation relationship:

[0084] ;

[0085] in, Indicates the first Variance calculation performed within each epoch, using commonly visible satellites as the statistical objects. This represents the variance extracted from the equivalent single-station oblique total electron content within the t-th epoch.

[0086] No. Within an epoch, the first The non-common error residual for extracting the equivalent single-station oblique total electron content corresponding to the three commonly visible satellites is:

[0087] ;

[0088] in, This represents the non-common error residual obtained from the equivalent single-station oblique total electron content extraction, derived from the inter-receiver station single-difference residual mapping. This error residual reflects the discrete component of the equivalent single-station non-common error after excluding the cross-satellite common hardware deviation difference at the receiver end, and does not represent the absolute error relative to the external true oblique total electron content.

[0089] Based on the non-common error residual of the equivalent single-station oblique total electron content extraction, the variance of the equivalent single-station oblique total electron content extraction is:

[0090] ;

[0091] Step S2 states: ;

[0092] Therefore, the specific formulas for extracting the variance and standard deviation of the equivalent single-station oblique total electron content in step S4 are as follows:

[0093] ;

[0094] ;

[0095] in, This represents the variance extracted from the equivalent single-station oblique total electron content within the t-th epoch. This represents the standard deviation of the single difference within the t-th epoch. This represents the standard deviation of the equivalent single-station oblique total electron content extracted within the t-th epoch.

[0096] S5: Within a preset time window, the variances of the equivalent single-station oblique total electron content extraction for each valid epoch are weighted and merged according to epoch weights to obtain the merged variance. The merged standard deviation is then calculated based on the merged variance, and this standard deviation is used as the accuracy evaluation result for the oblique total electron content extraction within the preset time window. The single-station oblique total electron content extraction accuracy evaluation result is used for ionospheric observation quality control, ionospheric correction product reliability evaluation, ambiguity fixation risk analysis, anomaly observation identification, or auxiliary evaluation of positioning service availability under space weather disturbance conditions in single-station high-precision, short-baseline high-precision, or global rapid high-precision positioning processing.

[0097] Specifically, the preset time window in step S5 can be an hourly window, a daily window, a monthly window, or a custom time window corresponding to a specific space weather event. The specific preset time window can be set to 5 minutes, 1 hour, 24 hours, or a custom time window corresponding to a space weather event. The epoch weight is determined based on the number of effective common visible satellites, the elevation angle statistics of common visible satellites, the carrier-to-noise ratio statistics, or the single-difference residual statistics for each epoch. When the evaluation purpose is anomaly observation suppression or robust window merging, the single-difference residual statistics weight is preferred; when the evaluation purpose is space weather disturbance identification, STEC accuracy degradation monitoring, or time series change analysis, the number of effective common visible satellites weight, elevation angle statistics weight, or carrier-to-noise ratio statistics weight is preferred to avoid excessively weakening the accuracy degradation characteristics caused by real disturbances.

[0098] Specifically, when the epoch weight is the weight of the number of effective commonly visible satellites, the specific formulas for the combined variance and combined standard deviation are as follows:

[0099] ;

[0100] ;

[0101] ;

[0102] Where T represents the set of valid epochs within the preset time window, Indicates the first Each epoch corresponds to an epoch weight. Indicates the first The number of effectively co-visible satellites within a given epoch. Indicates the first Variance extraction of the equivalent single-station oblique total electron content corresponding to each epoch. Indicates the combined variance. This represents the combined standard deviation.

[0103] When the epoch weight is a statistic of the elevation angle of the common visible satellites, the epoch weight can be expressed as:

[0104] ;

[0105] in, Indicates the first Within an epoch, the first The elevation angle of the three commonly visible satellites This is a preset index. The higher the elevation angle, the less the observation is affected by low elevation angle noise, multipath, and propagation path errors, so the corresponding epoch can be assigned a larger weight.

[0106] When the epoch weight is a carrier-to-noise ratio statistic, the epoch weight can be expressed as:

[0107] ;

[0108] in, Indicates by the first Within an epoch, the first The quality factor is determined by the carrier-to-noise ratio (CNR) of the three commonly visible satellites. A higher CNR indicates better signal tracking quality, and a larger weight is assigned to the corresponding epoch. Conversely, a lower CNR may result in increased observation noise, signal attenuation, or tracking errors, and a smaller weight is assigned to the corresponding epoch.

[0109] When the epoch weights are simple difference residual statistics, the epoch weights can be expressed as:

[0110] ;

[0111] in, Indicates the first Inter-station single difference within an epoch, standard deviation within an epoch. This represents the preset reference single-difference standard deviation. The greater the dispersion of the single-difference residual, the more likely there are observational anomalies, local multipath enhancement, signal quality degradation, or space weather disturbances within that epoch. Its weight in window merging can be reduced depending on the evaluation purpose.

[0112] Step S5 further includes: generating an ionospheric observation quality evaluation index based on the merged standard deviation. This ionospheric observation quality evaluation index is used for ionospheric observation quality control, ionospheric correction product reliability evaluation, ambiguity fixation risk analysis, anomaly observation identification, or positioning service availability assessment under space weather disturbance conditions in precise single-point positioning, real-time dynamic differential positioning, or precise single-point positioning real-time dynamic differential fusion positioning.

[0113] S6: Obtain the space weather index corresponding to each epoch, determine the geomagnetic quiet time window and the geomagnetic disturbance time window based on the space weather index, and obtain the corresponding merged standard deviation. Calculate the oblique total electron content extraction accuracy degradation rate based on the merged standard deviation corresponding to the geomagnetic quiet time window and the geomagnetic disturbance time window.

[0114] Let the pooled standard deviation of the geomagnetic quiet time window be... The combined standard deviation of the geomagnetic disturbance time window is The degradation rate of the extraction accuracy of total electron content by oblique direction Calculate according to the following formula:

[0115]

[0116] Based on the merged standard deviation or accuracy degradation rate, generate at least one of the following: accuracy versus time curve, space weather correlation results, extraction method comparison results, or positioning quality control identifier.

[0117] The beneficial effects of the present invention will be illustrated below through the following verification methods:

[0118] Verification Method 1:

[0119] The statistical distribution of single-day, single-difference ionospheric observations varies with the method of extracting oblique total electron content (STEC) and station conditions, illustrating that the traditional method's assumption of a uniform approximate normal distribution for accuracy conversion across all scenarios is not realistic.

[0120] Three methods were employed to extract the total oblique electron content (STEC): carrier phase smoothing pseudorange (CCL), non-differential uncombined precise point positioning floating-point solution (PPP floating-point solution), and non-differential uncombined precise point positioning fixed solution (PPP fixed solution). All three methods used GPS L1 and L2 carrier phase observations and P1 and P2 pseudorange observations at a sampling interval of 30 seconds, with a 15° elevation angle cutoff to mitigate the impact of low-elevation-angle observation noise. In PPP processing, the tropospheric delay dry component was corrected using the Saastamoinen model, while the wet component was estimated as a random walk parameter; ionospheric delay and receiver clock bias were modeled as white noise processes. For the non-differential uncombined precise point positioning fixed solution (PPP fixed solution), the carrier phase ambiguity was fixed using uncalibrated phase delay products provided by the International GNSS Monitoring and Evaluation System, and parameter estimation was performed using Kalman filtering.

[0121] We selected zero baselines EIL3-EIL4 and short baselines STJ3-STJO from 001 day of 2024 and plotted probability histograms, fitted normal probability density function curves, and standard normal QQ plots for the single-difference ionospheric observations obtained by the three extraction methods.

[0122] like Figure 2 As shown, the single-difference histogram obtained using the PPP floating-point solution for zero baseline EIL3-EIL4 is unimodal and approximately symmetrical. The sample points are basically distributed along the reference line in the QQ plot, deviating only slightly at extreme quantiles. Its skewness is approximately 0.047 and kurtosis is approximately 3.853, indicating that this group of samples can be approximated as a normal distribution. Meanwhile, the results of the CCL and PPP fixed solutions differ from those of the PPP floating-point solution in terms of tail shape, symmetry, and the degree of deviation in the QQ plot.

[0123] like Figure 3 As shown, the single-difference histogram obtained using the CCL method for the short baseline STJ3-STJO exhibits obvious multimodal and asymmetric characteristics, with a low degree of fit between the fitted normal probability density function and the sample distribution; the corresponding QQ plot is S-shaped, with both the low and high quantiles systematically deviating from the reference line. The histogram and QQ plot corresponding to the PPP fixed solution also show obvious non-normal characteristics. Therefore, whether the single-difference sample approximates normality depends not only on the extraction method but also on the station and baseline conditions.

[0124] Depend on Figure 2 and Figure 3 It is known that when the sample exhibits multiple peaks, skewness, long tails, or a clear trend, the accuracy indicators calculated based on the assumptions of all-day extreme values ​​and uniform normality are prone to distortion. In traditional methods, the peak-to-peak values ​​of daily single-difference ionospheric observations across different arc segments are used as the basis for these calculations. To determine the accuracy (i.e.) However, this formula holds true only if the receiver differential code bias (RDCB) remains constant throughout the day and the samples follow an approximately normal distribution. In reality, the receiver differential code bias (RDCB) changes significantly with temperature fluctuations, potentially introducing errors of up to 10-20 TECUs. This causes traditional evaluation accuracy to deviate significantly from the actual extraction performance.

[0125] The above results indicate that the distribution pattern of inter-station single differences changes with the method of extracting oblique total electron content, the station environment, and the baseline configuration. The method of this invention calculates the intra-epoch variance based on the residuals of inter-station single differences within the same epoch, without needing to convert the peak-to-peak value to the standard deviation based on the assumption of an approximately normal distribution of diurnal inter-station single differences. Therefore, it is applicable to the above-mentioned different distribution patterns of inter-station single differences.

[0126] Verification Method 2:

[0127] The effect of this method on suppressing such trend components is demonstrated by verifying the influence of receiver-side trend components on the STEC extraction accuracy evaluation.

[0128] Observational data from the short baseline (ZIM2-ZIMM) at DOY 99 and DOY 118 in 2024 were selected. STEC was extracted using either the carrier phase smoothing pseudorange method (CCL), the non-differential non-combined precise single-point positioning floating-point solution method (PPP floating-point solution), or the non-differential non-combined precise single-point positioning fixed solution method (PPP fixed solution), respectively. The results are as follows: Figure 4 The time series plots shown are presented, and the quantitative results are shown in Table 2.

[0129] Table 2

[0130]

[0131] like Figure 4As shown, the inter-station single-difference time series for year-end 099 is relatively stable overall, while the inter-station single-difference time series for year-end 118 shows a clear intraday upward trend. On year-end 118, the traditional diurnal scale assessment value increases significantly with the increase in trend amplitude, and the 24-hour pooled standard deviation obtained by the method of this invention remains at the same order of magnitude as the result for year-end 099. Referring to Table 2, for CCL, the traditional diurnal scale assessment value increases from 0.450 TECU to 1.038 TECU, and the pooled standard deviation obtained by the method of this invention changes from 0.240 TECU to 0.258 TECU; for the PPP floating-point solution, the traditional diurnal scale assessment value increases from 0.107 TECU to 0.474 TECU, and the pooled standard deviation obtained by the method of this invention changes from 0.049 TECU to 0.054 TECU; for the PPP fixed solution, the traditional diurnal scale assessment value increases from 0.071 TECU to 1.171 TECU, and the pooled standard deviation obtained by the method of this invention for both observation days is 0.006 TECU.

[0132] Furthermore, under DOY 118 conditions, the traditional evaluation values ​​of the carrier phase smoothing pseudorange method (CCL), the non-differential non-combined precise single-point positioning floating-point solution method (PPP floating-point solution), or the non-differential non-combined precise single-point positioning fixed solution (PPP fixed solution) are approximately 4.0 times, 8.8 times, and 195.2 times that of this method, respectively. This comparison illustrates that when there is an intraday trend in the inter-station single difference, the peak-to-peak difference between different arc segments is mainly dominated by the trend component, making it difficult to continue characterizing the random dispersion of the single difference. The method of this invention performs mean-removal processing on the inter-station single difference sequence within each epoch, resulting in approximately the same receiver-end common hardware deviation drift or trend component for each commonly visible satellite, without affecting the inter-station single difference residual and its dispersion statistics within the same epoch; the satellite-related non-common trend component is still retained in the inter-station single difference residual. Therefore, in this verification method, the intraday trend change of the inter-station single difference will not be directly included as the dispersion of non-common error in the accuracy evaluation result of this invention.

[0133] Verification Method 3:

[0134] This study demonstrates the compatibility of our extraction method with different STEC extraction methods, baseline types, and space weather conditions through experiments (stable and geomagnetic storm) on the impact of space weather environment on STEC extraction accuracy. It also verifies our ability to characterize the time-varying process of STEC extraction accuracy using a flexible time window. A higher STEC extraction accuracy value indicates a larger discrete error and lower extraction accuracy.

[0135] 1. Stable space weather conditions

[0136] The zero baseline GODZ-GODE and the short baseline USN7-WDC5 of 2024 year-end 001 were selected. The oblique total electron content observation values ​​were extracted using CCL, PPP floating-point solution and PPP fixed solution respectively, and the accuracy was evaluated according to the above steps S1 to S5.

[0137] like Figure 5 As shown, under both zero-baseline and short-baseline configurations, the dispersion of inter-station single differences decreases sequentially from CCL to PPP floating-point solution to PPP fixed solution. The method of this invention obtains accuracy assessment results for different oblique total electron content extraction methods without changing the accuracy assessment steps, and is applicable to both zero-baseline and short-baseline configurations. Specifically, the assessment results for zero-baseline mainly reflect non-common errors such as receiver observation noise, internal processing errors, and extraction method processing errors; the assessment results for short-baseline also include the effects of local multipath differences and residual propagation path differences.

[0138] 2. Geomagnetic disturbance conditions

[0139] Geomagnetic disturbances occurring between epoch 131 and 134 in 2024 were selected, during which the planetary Kp index peaked at 9. For the EIL3 station, the accuracy assessment results for epoch-level oblique total electron content extraction during epoch 120 to 139 in 2024 were calculated, and the ionospheric irregularity activity characterization index ROTI and the TEC rate of change index AATR along the satellite arc were simultaneously acquired. The results are as follows: Figure 6 As shown.

[0140] With the evaluation window set to 1 hour, hourly STEC extraction accuracy indices were calculated for zero baseline EIL3-EIL4 and short baselines YELL-YEL2, KIR0-KIR8, and STJ3-STJO. The results are as follows: Figure 7 As shown in Table 3.

[0141] Table 3

[0142]

[0143] like Figure 6 and Figure 7 As shown, after the year 131 of 2024, the accuracy assessment results of the total electron content extraction increased, and a peak was formed near the year 132; ROTI and AATR increased synchronously during the corresponding period.

[0144] As shown in Table 3, compared with the quiet day DOY 128, the maximum hourly combined standard deviation of EIL3-EIL4, KIR0-KIR8, STJ3-STJO and YELL-YEL2 during the disturbance period increased from 0.035 TECU, 0.309 TECU, 0.085 TECU and 0.193 TECU to 0.417 TECU, 0.621 TECU, 0.302 TECU and 0.598 TECU, respectively, with corresponding maximum accuracy degradation rates of 1091.4%, 101.0%, 255.3% and 209.8%.

[0145] In this verification method, the accuracy-time curve generated by the result output module has corresponding variation characteristics with the time series of ROTI and AATR. Therefore, the merged standard deviation or accuracy degradation rate can be used to generate space weather correlation results or ionospheric observation quality indicators. Without changing the evaluation steps of this invention, the preset time window can also be set to daily, monthly, or a custom time window corresponding to a specified space weather event.

[0146] An evaluation system for assessing the accuracy of ionospheric oblique total electron content extraction using a method based on single-difference between co-located stations includes:

[0147] The data acquisition module is used to acquire the oblique total electron content observation values ​​of two co-located receivers using the same satellite navigation system within the same epoch for the same batch of common visible satellites under the same signal or frequency conditions.

[0148] The inter-station single difference construction module is used to calculate the inter-station single difference value for each commonly visible satellite in the same batch within the same epoch of two satellite navigation system receivers in turn, thereby obtaining the inter-station single difference value for each commonly visible satellite in the same batch. The inter-station single difference values ​​in the same batch constitute the inter-station single difference sequence of the commonly visible satellites in the same batch within one epoch.

[0149] The epoch-by-epoch variance statistics module is used to calculate the mean of the inter-station single difference sequence for the same batch of commonly visible satellites within an epoch. The mean of the inter-station single difference sequence is used to perform intra-epoch centering processing on the inter-station single difference sequence to eliminate the cross-satellite common component of the common hardware deviation difference and obtain the single difference residual sequence. Based on the single difference residual sequence, the intra-epoch variance and intra-epoch standard deviation of the inter-station single difference are calculated. The intra-epoch variance of the inter-station single difference is used as a cross-satellite dispersion statistic of the difference between the non-common error of the oblique total electron content extraction of two receivers within an epoch.

[0150] The single-station accuracy mapping module is used to map the cross-satellite dispersion of the difference between the non-common errors in the oblique total electron content extraction of two receivers to the equivalent single-station oblique total electron content extraction non-common error based on the variance within the single epoch of inter-station differences and the error propagation relationship. It also calculates the equivalent single-station oblique total electron content extraction variance and the equivalent single-station oblique total electron content extraction standard deviation. The smaller the combined standard deviation, the smaller the dispersion of the non-common error in the oblique total electron content extraction, and the higher the corresponding oblique total electron content extraction accuracy.

[0151] The time window merging module is used to perform weighted merging of the variance of the equivalent single-station oblique total electron content extraction for each effective epoch within a preset time window, according to the epoch weight, to obtain the merged variance, and calculate the merged standard deviation based on the merged variance, and use the merged standard deviation as the evaluation result of the oblique total electron content extraction accuracy corresponding to the preset time window.

[0152] In practical applications, a result output module can also be set up according to needs to output accuracy change curves over time, spatial weather correlation results, algorithm comparison results, or positioning quality control indicators.

[0153] Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

Claims

1. A method for evaluating the accuracy of ionospheric oblique total electron content extraction based on single difference between co-located stations, characterized in that, Specifically, the following steps are included: S1: Obtain the oblique total electron content observation values ​​of two co-located receivers using the same satellite navigation system within the same epoch for the same batch of common visible satellites under the same signal or frequency conditions; S2: By sequentially calculating the inter-station single difference value for each commonly visible satellite in the same batch within the same epoch of two satellite navigation system receivers, the inter-station single difference value of each commonly visible satellite in the same batch is obtained. The inter-station single difference values ​​of the same batch constitute the inter-station single difference sequence of the commonly visible satellites in the same batch within one epoch. S3: Calculate the mean of the inter-station single difference sequence for the same batch of commonly visible satellites within an epoch; use the mean of the inter-station single difference sequence to perform intra-epoch centering processing on the inter-station single difference sequence to eliminate the cross-satellite common component of the common hardware deviation difference and obtain the single difference residual sequence; calculate the intra-epoch variance and intra-epoch standard deviation of the inter-station single difference based on the single difference residual sequence; use the intra-epoch variance of the inter-station single difference as a cross-satellite dispersion statistic of the difference between the non-common errors extracted by the oblique total electron content of two receivers within an epoch; S4: Based on the variance within the single epoch of the inter-station difference and the error propagation relationship, the cross-satellite dispersion of the difference between the non-common errors of the oblique total electron content extraction of the two receivers is mapped to the equivalent single-station oblique total electron content extraction non-common error, and the equivalent single-station oblique total electron content extraction variance and the equivalent single-station oblique total electron content extraction standard deviation are calculated. S5: Within a preset time window, the variance of the equivalent single-station oblique total electron content extraction for each effective epoch is weighted and merged according to the epoch weight to obtain the merged variance. The merged standard deviation is then calculated based on the merged variance, and the merged standard deviation is used as the evaluation result of the oblique total electron content extraction accuracy for the preset time window.

2. The method for evaluating the accuracy of ionospheric oblique total electron content extraction based on single difference between co-located stations as described in claim 1, characterized in that: The oblique total electron content observation value in step S1 is obtained by processing the satellite's dual-frequency pseudorange observation value and dual-frequency carrier phase observation value through an oblique total electron content extraction method. The oblique total electron content extraction method includes the carrier phase smoothing pseudorange method, the non-differential non-combined precise single-point positioning floating-point solution method, or the non-differential non-combined precise single-point positioning fixed solution method.

3. The method for evaluating the accuracy of ionospheric oblique total electron content extraction based on single difference between co-located stations as described in claim 1, characterized in that: The specific formulas for the mean of the single-difference sequence, the single-difference residual, and the intra-epoch variance of the inter-station single-difference sequence in step S3 are as follows: ； ； ； ； in, Let represent the mean of the inter-station single-difference sequence of the same batch of commonly visible satellites within the t-th epoch, where t represents the epoch number. This represents the number of commonly visible satellites within the t-th epoch, where j represents the index of the commonly visible satellite. This represents the inter-station single difference value of the j-th commonly visible satellite within the t-th epoch. Indicates the first Within an epoch, the first Single-difference residuals of three commonly visible satellites This represents the inter-station single difference within the epth epth . Indicates the first The station-to-station single difference and standard deviation within an epoch are calculated within one epoch; the above calculation process is completed within one epoch.

4. The method for evaluating the accuracy of ionospheric oblique total electron content extraction based on single difference between co-located stations as described in claim 1, characterized in that: The specific formulas for calculating the variance and standard deviation of the equivalent single-station oblique total electron content extraction in step S4 are as follows: ； ； in, This represents the variance extracted from the equivalent single-station oblique total electron content within the t-th epoch. This represents the standard deviation of the single difference within the t-th epoch. This represents the standard deviation of the equivalent single-station oblique total electron content extracted within the t-th epoch.

5. The method for evaluating the accuracy of ionospheric oblique total electron content extraction based on single difference between co-located stations as described in claim 1, characterized in that, The preset time window in step S5 is specifically: an hourly window, a daily window, a monthly window, or a custom time window corresponding to a specific spatial weather event.

6. The method for evaluating the accuracy of ionospheric oblique total electron content extraction based on single difference between co-located stations as described in claim 1, characterized in that, The epoch weights in step S5 are determined based on the number of effective common visible satellites in each epoch, the common visible satellite elevation angle statistics, the carrier-to-noise ratio statistics, or the single-difference residual statistics.

7. The method for evaluating the accuracy of ionospheric oblique total electron content extraction based on single difference between co-located stations as described in claim 6, characterized in that, When the epoch weight is the weight of the number of effective commonly visible satellites, the specific formulas for the combined variance and combined standard deviation are as follows: ； ； ； Where T represents the set of valid epochs within the preset time window, Indicates the first Each epoch corresponds to an epoch weight. Indicates the first The number of commonly visible satellites within a single epoch. Indicates the first Variance extraction of the equivalent single-station oblique total electron content corresponding to each epoch. Indicates the combined variance. This represents the combined standard deviation.

8. The method for evaluating the accuracy of ionospheric oblique total electron content extraction based on single difference between co-located stations as described in claim 1, characterized in that, Also includes: S6: Obtain the space weather index corresponding to each epoch, determine the geomagnetic quiet time window and the geomagnetic disturbance time window based on the space weather index, and obtain the corresponding merged standard deviation. Calculate the oblique total electron content extraction accuracy degradation rate based on the merged standard deviation corresponding to the geomagnetic quiet time window and the geomagnetic disturbance time window.

9. The method for evaluating the accuracy of ionospheric oblique total electron content extraction based on single difference between co-located stations as described in claim 1, characterized in that, Step S5 further includes: generating an ionospheric observation quality evaluation index based on the merged standard deviation.

10. An evaluation system for assessing the accuracy of ionospheric oblique total electron content extraction based on single difference between co-located stations as described in any one of claims 1 to 9, characterized in that, include: The data acquisition module is used to acquire the oblique total electron content observation values ​​of two co-located receivers using the same satellite navigation system within the same epoch for the same batch of common visible satellites under the same signal or frequency conditions. The inter-station single difference construction module is used to calculate the inter-station single difference value for each commonly visible satellite in the same batch within the same epoch of two satellite navigation system receivers in turn, thereby obtaining the inter-station single difference value for each commonly visible satellite in the same batch. The inter-station single difference values ​​in the same batch constitute the inter-station single difference sequence of the commonly visible satellites in the same batch within one epoch. The epoch-by-epoch variance statistics module is used to calculate the mean of the inter-station single difference sequence for the same batch of commonly visible satellites within an epoch. The mean of the inter-station single difference sequence is used to perform intra-epoch centering processing on the inter-station single difference sequence to eliminate the cross-satellite common component of the common hardware deviation difference and obtain the single difference residual sequence. Based on the single difference residual sequence, the intra-epoch variance and intra-epoch standard deviation of the inter-station single difference are calculated. The intra-epoch variance of the inter-station single difference is used as a cross-satellite dispersion statistic of the difference between the non-common error of the oblique total electron content extraction of two receivers within an epoch. The single-station accuracy mapping module is used to map the cross-satellite dispersion of the difference between the non-common errors of the oblique total electron content extraction of two receivers to the equivalent single-station oblique total electron content extraction non-common error based on the variance within the single epoch of the inter-station single difference and the error propagation relationship, and to calculate the equivalent single-station oblique total electron content extraction variance and the equivalent single-station oblique total electron content extraction standard deviation. The time window merging module is used to perform weighted merging of the variance of the equivalent single-station oblique total electron content extraction for each effective epoch within a preset time window, according to the epoch weight, to obtain the merged variance, and calculate the merged standard deviation based on the merged variance, and use the merged standard deviation as the evaluation result of the oblique total electron content extraction accuracy corresponding to the preset time window.

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