Method for constructing a receiver tracking error stochastic model based on ionospheric scintillation index

Abstract

The application provides a receiver tracking error random model construction method based on an ionospheric scintillation index, comprising the following steps: detecting a precise cycle slip, de-trending an SG filtered carrier phase observation value, and calculating a scintillation index based on 1Hz data of a common GNSS receiver; a new receiver tracking error random model suitable for ionospheric scintillation suppression of the common GNSS receiver is constructed; the problem that positioning accuracy of the common GNSS receiver is reduced or even unavailable under ionospheric scintillation conditions is solved; and high-precision positioning under ionospheric scintillation conditions is realized.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation technology, and in particular to a method for constructing a random model of receiver tracking error based on the ionospheric scintillation index. Background Technology

[0002] Ionospheric scintillation is a phenomenon where the amplitude and phase of radio signals fluctuate rapidly and randomly when they pass through irregular regions of the ionosphere. It is prevalent in low-latitude regions, auroral areas, and polar regions, with particularly intense scintillation occurring several hours after sunset. It not only degrades the quality of Global Navigation Satellite System (GNSS) observations, but moderate to strong ionospheric scintillation can also lead to frequent cycle slips and even GNSS signal loss. When multiple GNSS satellites are simultaneously subjected to severe ionospheric scintillation interference, navigation and positioning may become unavailable in certain areas for a period of time, severely impacting GNSS positioning performance and operational efficiency.

[0003] To identify and determine ionospheric scintillation and its intensity, researchers have proposed various scintillation indices and intensity classification criteria, constructed corresponding stochastic models, and attempted to conduct research and applications on ionospheric scintillation suppression. Ionospheric scintillation can be divided into amplitude scintillation and phase scintillation (Beach and Kintner, 1999), both of which are essentially signal diffraction effects, and their scintillation intensities are determined by... index and The indices are determined. Typically, these indices can be obtained directly from dedicated ionospheric scintillation monitoring receivers (ISMRs) with a 50 Hz time resolution. However, due to the extremely high storage requirements and cost of ISMRs, they are not widely deployed in large-scale or global GNSS networks. Literature review reveals that phase scintillation indices... It can be calculated based on the original carrier phase observations within the detrended cycle-slip-free period, but the amplitude scintillation index... This data needs to be output by ISMRs and cannot be acquired by ordinary receivers with low sampling rates. Therefore, Luo et al. (2020) conducted a study based on 1Hz data from a conventional geodetic GNSS receiver, using carrier-to-noise ratio (CNR) data. C / No Related research on calculating the amplitude scintillation index using the carrier-to-noise density ratio (C / No) has been conducted, and a new amplitude scintillation index based on the carrier-to-noise ratio is referred to as... Index. Statistical results show that during the flickering period, the index obtained from a regular receiver... Index and generated by ISMRs The correlation coefficient between indices is usually higher than 0.9, therefore it can be used Exponential approximation The index enables ionospheric scintillation monitoring based on ordinary GNSS receivers.

[0004] To address ionospheric scintillation suppression, common stochastic models such as the Elevation Angle Stochastic (EAS) model cannot assign appropriate weights to GNSS observations affected by ionospheric scintillation because scintillation can affect satellites at any elevation angle, including those greater than 50°. In contrast to the EAS model, Luo et al. (2022) used GPS data from IGS (International GNSS Service) high-latitude stations to... The model was weighted, and the experimental results showed that... The model also performed poorly during ionospheric scintillation. Compared to the EAS model and... Compared to the limitations of traditional models during ionospheric scintillation, the Receiver Tracking Error Stochastic (RTES) model can mitigate the impact of ionospheric scintillation on precise GNSS positioning (Conker et al., 2003). This model fully considers the impact of different types of scintillation and their intensity on the receiver delay-locked loop (DLL) and phase-locked loop (PLL), calculates the tracking errors of the receiver DLL and PLL, and can assign appropriate weights to GNSS observations during ionospheric scintillation, thereby improving positioning accuracy. Multiple studies have demonstrated that the RTES model can significantly improve RTK and PPP positioning accuracy during ionospheric scintillation (Aquino et al., 2009; da Silva et al., 2010). Inspired by the RTES model, Luo et al. (2023) established an improved RTES model for GPS systems based on ordinary GNSS receivers, namely the Impr_RTES model. Experimental results show that this model significantly improves GPS single-frequency PPP positioning accuracy compared to the EAS model during ionospheric scintillation. This is because the Impr_RTES model constructs the PLL tracking error based on the Rate of Total Electron Content Index (ROTI), rather than the phase scintillation index calculated from the original observations. Therefore, there are some differences between the RTES model constructed from the output values ​​of ISMRs and the model constructed from them. Summary of the Invention

[0005] This invention provides a method for constructing a random model of receiver tracking error based on the ionospheric scintillation index, which addresses the deficiencies in existing technologies. It enables the extraction of amplitude scintillation index and phase scintillation index from observation data at a specified frequency output by a common GNSS receiver. Based on the scintillation index and the concept of RTES model construction for GPS systems, an ionospheric scintillation suppression RTES model suitable for common GNSS receivers is established to improve GNSS positioning accuracy under ionospheric scintillation conditions.

[0006] In a first aspect, the present invention provides a method for constructing a random model of receiver tracking error based on the ionospheric scintillation index, comprising:

[0007] At the same location and within the same time period, raw GNSS observations were collected using a GNSS receiver at a preset sampling rate, and ionospheric observation data were collected using a dedicated ionospheric scintillation monitoring receiver.

[0008] Based on the TurboEdit algorithm, cycle slip detection is performed on the original carrier phase observations in the original GNSS observations, and the carrier phase observations during the cycle slip-free period are output.

[0009] The carrier phase observations during the cycle-slip-free period are detrended using a polynomial smoothing method to obtain the detrended carrier phase observations.

[0010] Based on the carrier-to-noise ratio data of the preset frequency of the GNSS receiver and the detrended carrier phase observation value, the new amplitude scintillation index and phase scintillation index are calculated.

[0011] For the cycle slip period, based on the scintillation index output by the dedicated ionospheric scintillation receiver, the variance of pseudorange and carrier phase observations is calculated using a classical receiver tracking error stochastic model. The proportional relationship between the variance of pseudorange observations and the variance of carrier phase observations under different scintillation intensities is determined. The variance of phase observations during the cycle slip period is determined by using the proportional relationship between the pseudorange variance calculated by the new amplitude scintillation index and the variance of pseudorange and phase observations.

[0012] For cycle-slip-free periods, a scintillation variance calculation formula is established using the new amplitude scintillation index and the phase scintillation index, and a receiver tracking error stochastic model suitable for GNSS receivers is constructed to obtain GNSS positioning results under ionospheric scintillation conditions.

[0013] According to the present invention, a method for constructing a random model of receiver tracking error based on ionospheric scintillation index is provided. This method uses the TurboEdit algorithm to perform cycle slip detection on the original carrier phase observations in the original GNSS observations, and outputs the carrier phase observations during cycle slip-free periods, including:

[0014] The TurboEdit algorithm includes the MW combined cycle slip algorithm and the GF combined cycle slip algorithm;

[0015] The MW combined cycle slip algorithm performs cycle slip detection on the original carrier phase observation values ​​and outputs wide-term cycle slip detection values.

[0016] The GF combined cycle slip algorithm performs cycle slip detection on the original carrier phase observation values ​​and outputs narrow term cycle slip detection values.

[0017] The wide-term cycle slip detection values ​​and narrow-term cycle slip detection values ​​of each epoch are screened separately. Carrier phase observation values ​​corresponding to the epochs in which cycle slips occur are removed, and carrier phase observation values ​​in the period without cycle slips are retained.

[0018] According to the present invention, a method for constructing a random model of receiver tracking error based on the ionospheric scintillation index is provided. A polynomial smoothing method is used to detrend the carrier phase observations during the cycle-slip-free period to obtain detrended carrier phase observations, including:

[0019] Within a sliding window, multiple carrier phase observations are fitted to construct a matrix that includes the fitting coefficients of a polynomial of any order, the fitting error at any time, and the carrier phase observation at any time.

[0020] The sliding window size and matrix order are determined, and the fitting coefficient vector is obtained by solving the least squares algorithm. The carrier phase observations within the sliding window are weighted and filtered in cycles to obtain the detrended carrier phase observations.

[0021] According to the present invention, a method for constructing a random model of receiver tracking error based on ionospheric scintillation index is provided. Based on carrier-to-noise ratio data at a preset frequency of the GNSS receiver and the detrended carrier phase observations, a new amplitude scintillation index and a phase scintillation index are calculated, including:

[0022] Carrier-to-noise ratio (CNR) data is obtained from the RINEX observation files of the GNSS receiver. Signal-to-noise ratio (SNR) data is calculated from the CNR data. Detrended signal strength is calculated from the SNR data. New amplitude scintillation index is obtained based on the detrended signal strength.

[0023] The detrended carrier phase observations are subjected to mean correlation processing to obtain the phase flicker index.

[0024] According to the present invention, a method for constructing a random model of receiver tracking error based on ionospheric scintillation index, after calculating the new amplitude scintillation index and phase scintillation index based on carrier-to-noise ratio data of a preset frequency of a GNSS receiver and the detrended carrier phase observation, further includes:

[0025] The tracking error variance of the delay-locked loop is obtained from the single-sided bandwidth of the delay-locked loop of the GNSS receiver, the spacing between the C / A chip correlators, the pre-detection integration time of the delay-locked loop, the signal-to-noise ratio data, and the amplitude scintillation index.

[0026] The phase-locked loop tracking error variance is obtained from the equivalent loop bandwidth of the phase-locked loop single-sided noise, the phase-locked loop pre-detection integration time, the signal-to-noise ratio data, the amplitude scintillation index, the spectral intensity of the phase noise at the preset frequency, the phase-locked loop order, the loop natural frequency, the slope of the power spectral density of the detrended phase observation value within the preset frequency range around the signal frequency point, and the oscillator noise of the GNSS receiver.

[0027] The pseudorange observation weight and the carrier phase observation weight are obtained by calculating the variance of the tracking error of the delay-locked loop and the reciprocal of the variance of the tracking error of the phase-locked loop, respectively.

[0028] Replace the amplitude scintillation index in the calculation of the tracking error variance of the delay-locked loop and the tracking error variance of the phase-locked loop with a new amplitude scintillation index to determine the new tracking error variance of the delay-locked loop and the thermal noise variance component in the tracking error variance of the phase-locked loop.

[0029] According to the present invention, a method for constructing a random model of receiver tracking error based on the ionospheric scintillation index is provided. For the cycle slip period, based on the scintillation index output by the dedicated ionospheric scintillation receiver, the variances of pseudorange and carrier phase observations are calculated using a classical random model of receiver tracking error. The proportional relationship between the variance of pseudorange observations and the variance of carrier phase observations under different scintillation intensities is determined. Using the proportional relationship between the variance of pseudorange during the cycle slip period calculated by the new amplitude scintillation index and the variances of pseudorange and phase observations, the variance of phase observations during the cycle slip period is determined, including:

[0030] Based on the scintillation index output by a dedicated ionospheric scintillation receiver, the variances of pseudorange and carrier phase observations are calculated using a classical receiver tracking error stochastic model.

[0031] Under different scintillation intensities, the proportional relationship between the variance of the pseudorange observations and the variance of the carrier phase observations was determined.

[0032] The variance of the pseudorange during the cycle slip period is calculated using the new amplitude scintillation index, and the proportional relationship between the pseudorange and the variance of the phase observation is used to obtain the variance of the phase observation during the cycle slip period by multiplying the pseudorange variance by the proportional relationship.

[0033] According to the present invention, a method for constructing a random model of receiver tracking error based on ionospheric scintillation index is provided. For cycle-slip-free periods, a scintillation variance calculation formula is established using the new amplitude scintillation index and the phase scintillation index to construct a random model of receiver tracking error suitable for GNSS receivers, thereby obtaining GNSS positioning results under ionospheric scintillation conditions. The method includes:

[0034] The phase-locked loop tracking error variance includes the thermal noise variance component, the phase flicker noise variance component, and the receiver oscillator noise variance component, wherein the receiver oscillator noise variance component is a constant.

[0035] A formula for calculating the scintillation variance of the phase scintillation noise variance component is established based on the phase scintillation index, thereby constructing a random model of receiver tracking error suitable for GNSS receivers;

[0036] Error estimation is performed using the receiver tracking error stochastic model to obtain GNSS positioning results under ionospheric scintillation conditions.

[0037] Secondly, the present invention also provides a system for constructing a random model of receiver tracking error based on the ionospheric scintillation index, comprising:

[0038] The acquisition module is used to acquire raw GNSS observations at a preset sampling rate using a GNSS receiver at the same location and within the same time period, and to acquire ionospheric observation data using a dedicated ionospheric scintillation monitoring receiver.

[0039] The detection module is used to perform cycle slip detection on the original carrier phase observations in the original GNSS observations based on the TurboEdit algorithm, and output the carrier phase observations during the cycle slip-free period.

[0040] The processing module is used to perform detrending processing on the carrier phase observations during the cycle-slip-free period using a polynomial smoothing method to obtain the detrending carrier phase observations.

[0041] The calculation module is used to calculate the new amplitude scintillation index and phase scintillation index based on the carrier-to-noise ratio data of the preset frequency of the GNSS receiver and the detrended carrier phase observation value;

[0042] The first construction module is used to calculate the variance of pseudorange and carrier phase observations based on the scintillation index output by the dedicated ionospheric scintillation receiver during the cycle slip period using a classical receiver tracking error stochastic model. It determines the proportional relationship between the variance of pseudorange observations and the variance of carrier phase observations under different scintillation intensities. It then uses the proportional relationship between the variance of pseudorange during the cycle slip period calculated by the new amplitude scintillation index and the variance of pseudorange and phase observations to determine the variance of phase observations during the cycle slip period.

[0043] The second construction module is used to establish a scintillation variance calculation formula using the new amplitude scintillation index and the phase scintillation index for cycle-slip-free periods, and to construct a receiver tracking error stochastic model suitable for GNSS receivers, so as to obtain GNSS positioning results under ionospheric scintillation conditions.

[0044] Thirdly, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the receiver tracking error stochastic model construction method based on the ionospheric scintillation index as described above.

[0045] Fourthly, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the receiver tracking error stochastic model construction method based on the ionospheric scintillation index as described above.

[0046] The method for constructing a random model of receiver tracking error based on the ionospheric scintillation index provided by this invention has the following beneficial effects:

[0047] (1) Establishing an RTES model applicable to ordinary GNSS receivers: The construction of classic RTES models relies on data from dedicated ionospheric scintillation monitoring receivers, while the new RTES model constructed in this invention can be applied to ordinary GNSS receivers, thus improving the usability of the new RTES model.

[0048] (2) Improve the positioning accuracy of ordinary GNSS receivers under ionospheric scintillation conditions: There is currently no random model for ionospheric scintillation suppression applicable to ordinary GNSS receivers. The novel random model constructed in this invention effectively weakens the impact of ionospheric scintillation on ordinary GNSS receivers and improves the positioning accuracy of ordinary GNSS receivers under ionospheric scintillation conditions.

[0049] (3) Significantly reduce the cost of high-precision positioning under ionospheric scintillation conditions: The classic RTES model relies on ISMR receivers, but ISMR receivers are expensive, which keeps the cost of ionospheric scintillation suppression high. A new RTES model based on the scintillation index calculated from 1Hz data of ordinary GNSS receivers is applicable to ordinary GNSS receivers and can significantly reduce the cost of high-precision GNSS positioning under ionospheric scintillation conditions. Attached Figure Description

[0050] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0051] Figure 1 This is one of the flowcharts illustrating the method for constructing a random model of receiver tracking error based on the ionospheric scintillation index provided by the present invention.

[0052] Figure 2 This is the second flowchart of the method for constructing a random model of receiver tracking error based on the ionospheric scintillation index provided by the present invention.

[0053] Figure 3 This is a schematic diagram of the receiver tracking error stochastic model construction system based on the ionospheric scintillation index provided by the present invention;

[0054] Figure 4 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0056] Under ionospheric scintillation conditions, GNSS positioning accuracy is severely affected, and constructing a stochastic model that can suppress ionospheric scintillation is difficult. Specific technical problems include:

[0057] Poor quality of observation data: Ionospheric scintillation can cause amplitude and phase scintillation of GNSS signals, thereby reducing the quality of observation data;

[0058] Frequent cycle slips lead to data discontinuity: Severe ionospheric scintillation causes GNSS receiver signal loss, resulting in frequent integer cycle count jumps or interruptions in carrier phase observations, posing a severe challenge to cycle slip detection and repair.

[0059] Constructing a stochastic model for ionospheric scintillation suppression is difficult: Under ionospheric scintillation conditions, the RTES model depends on ISMRs, so it is urgent to construct a stochastic model of receiver tracking error based on ordinary GNSS receivers to suppress the effects of ionospheric scintillation.

[0060] Figure 1This is one of the flowcharts illustrating the method for constructing a random model of receiver tracking error based on the ionospheric scintillation index provided in this invention. Figure 1 As shown, it includes:

[0061] Step 100: At the same location and within the same time period, use a GNSS receiver to collect raw GNSS observations at a preset sampling rate, and use a dedicated ionospheric scintillation monitoring receiver to collect ionospheric observation data.

[0062] Step 200: Perform cycle slip detection on the original carrier phase observations in the original GNSS observations based on the TurboEdit algorithm, and output the carrier phase observations during the cycle slip-free period;

[0063] Step 300: Use a polynomial smoothing method to detrend the carrier phase observations during the cycle-slip-free period to obtain detrendened carrier phase observations;

[0064] Step 400: Based on the carrier-to-noise ratio data of the preset frequency of the GNSS receiver and the detrended carrier phase observation value, calculate the new amplitude scintillation index and phase scintillation index;

[0065] Step 500: For the cycle slip period, based on the scintillation index output by the dedicated ionospheric scintillation receiver, calculate the variance of pseudorange and carrier phase observations using the classical receiver tracking error stochastic model, determine the proportional relationship between the variance of pseudorange observations and the variance of carrier phase observations under different scintillation intensities, and determine the variance of phase observations during the cycle slip period by using the proportional relationship between the pseudorange variance calculated by the new amplitude scintillation index and the variance of pseudorange and phase observations;

[0066] Step 600: For the cycle-slip-free period, use the new amplitude scintillation index and the phase scintillation index to establish a scintillation variance calculation formula, and construct a receiver tracking error stochastic model suitable for GNSS receivers to obtain GNSS positioning results under ionospheric scintillation conditions.

[0067] Specifically, the main implementation principles of the embodiments of the present invention are as follows: Figure 2 As shown, it includes:

[0068] Step 1: Use a standard GNSS receiver at a specified frequency, typically 1 Hz, to acquire raw GNSS observations, including pseudorange observations, carrier phase observations, and carrier-to-noise ratio (CNR). Simultaneously, use a dedicated ionospheric scintillation monitoring receiver installed at the same location to acquire data for the same time period. Use the TurboEdit algorithm to perform cycle slip detection on the 1 Hz raw carrier phase observations output by the standard GNSS receiver to determine the carrier phase observations during cycle slip-free periods.

[0069] Step 2: Use the polynomial smoothing method (Savitzky-Golay filtering, i.e., SG filtering) to detrend the carrier phase observations within the cycle-slip-free period determined in Step 1, and obtain the detrended carrier phase observations.

[0070] Step 3: Based on the 1Hz carrier-to-noise ratio (C / N0) data from a standard GNSS receiver and the carrier phase observation data obtained in Step 2, calculate the new amplitude scintillation index. and phase flicker index .

[0071] Step 4: For the cycle slip period, based on the true amplitude scintillation index and phase scintillation index collected by the ISMRs receiver in Step 1, calculate the corresponding pseudorange observation variance and carrier phase observation variance. Following the conventional approach of scaling up the initial pseudorange and initial phase variances proportionally, calculate the proportional relationship between the pseudorange observation variance and carrier phase observation variance under different scintillation intensities. Then, utilize the data obtained in Step 3... The pseudorange variance calculated by the exponent determines the phase variance. For cycle-slip-free periods, the phase variance is determined based on the variance obtained in step three. index and Based on the concept of RTES model construction, a new RTES model suitable for ordinary GNSS receivers is established to obtain GNSS positioning results under ionospheric scintillation conditions.

[0072] Therefore, this invention extracts the amplitude scintillation index and phase scintillation index from observation data at a specified frequency, typically 1Hz, output by a common GNSS receiver. Based on the scintillation index and the concept of RTES model construction for GPS systems, it establishes an ionospheric scintillation suppression RTES model suitable for common GNSS receivers, in order to improve GNSS positioning accuracy under ionospheric scintillation conditions.

[0073] Based on the above embodiments, the basic GNSS observation equations are given, laying the foundation for subsequent work.

[0074] The original GNSS pseudorange ( ) and phase ( The observed values ​​can be expressed as:

[0075] (1)

[0076] In the formula, and The first Pseudorange and carrier phase observations at each frequency point, in meters; Indicates the phase center of the satellite antenna ( s ) and receiver antenna phase center ( r The geometric distance, in meters; and This indicates the clock difference between the receiver and the satellite, expressed in meters. The wetted tropospheric delay at the zenith is measured in meters. This represents the projection function corresponding to the wet delay in the zenith troposphere; The ionospheric delay at the first signal frequency, in meters; Represents the ionospheric mapping factor, and , The first frequency point For the first Each frequency point; Indicates the first Each frequency point signal wavelength; The carrier phase ambiguity is expressed as an integer cycle, in cycles. and The pseudorange hardware delay between the receiver and the satellite is expressed in meters and is generally considered to be relatively stable over a day or a continuous arc segment. and These represent the phase hardware delay at the receiver and satellite, respectively, in weeks. They can be divided into a constant part and a time-varying part, where the constant part can be completely absorbed by the ambiguity parameter. and This is the sum of observation noise and multipath on pseudorange and phase observations.

[0077] It is worth noting that the tropospheric delay along the propagation path, whether wet or dry, can be expressed as the product of the zenith tropospheric delay and the corresponding projection function. The dry component of the tropospheric delay is usually corrected using prior models, such as the Saastamoinen model, and therefore will not be given here. The wet component of the tropospheric delay, however, has significant uncertainty and is difficult to model precisely. It is negligible in Standard Point Positioning (SPP) and short-range Real-Time Kinematic (RTK), but not negligible in long-range RTK, Precise Point Positioning (PPP), and PPP-RTK. Therefore, the wet component is usually obtained through estimation. Other errors, such as relativistic effects, need to be corrected using existing models. For PPP and PPP-RTK, it is also necessary to consider errors such as phase center offset (PCO) and phase offset variation (PCV) of antennas at the satellite and receiver ends, solid tides, ocean tides and polar tides, and phase entanglement, and to correct them using existing error models.

[0078] The TurboEdit algorithm in step one, originally proposed by Blewitt, combines two cycle slip detection algorithms: the Melbourne-Wübbena (MW) combination and the Geometry-Free (GF) combination. It boasts high detection accuracy and ease of implementation, thus finding widespread application and research use. The MW combination is primarily used for detecting wide-term cycle slips, while the GF combination is used for detecting narrow-term cycle slips. Finally, the cycle slip on the carrier is calculated based on the wide-term and narrow-term cycle slip values.

[0079] (1) MW combined detection cycle slip

[0080] Observation model of MW combination for:

[0081] (2)

[0082] In the formula, , These represent the first and second frequency points, respectively. , express , The corresponding carrier phase observations, in weeks; , They represent , The corresponding pseudorange observations are in meters; and These represent the broad term wavelength and broad term ambiguity, respectively. When cycle slip does not occur, It should be close to a constant and randomly distributed. The cycle slip test metric is constructed as follows:

[0083] (3)

[0084] Each epoch is calculated using a recursive formula. Average wide-term ambiguity and root mean square:

[0085] (4)

[0086] (5)

[0087] In the formula, For the front Individual epoch-wide fuzziness, For the front The average value of the epoch-level wide term ambiguity. For the front The average value of the epoch-level wide term ambiguity; Indicates the preceding The variance of each epoch, Indicates the preceding The variance of each epoch. If the following condition is met, then the current epoch is considered to have a cycle slip.

[0088] (6)

[0089] in, For the front The standard deviation of each epoch.

[0090] For carrier phase observations at two epochs, if the difference between them does not satisfy the cycle slip condition, then the carrier phase observation at that epoch is considered to be free of cycle slips. Conversely, if the difference satisfies the cycle slip condition, then the epoch is considered to have a cycle slip and is marked for removal in subsequent data processing. This process will be repeated to check whether cycle slips exist in the carrier phase observations at each epoch.

[0091] (2) GF combination detection cycle slip

[0092] Observation equations of the GF combination It can be represented as:

[0093] (7)

[0094] In the formula, and for , Ionospheric delay at two frequencies; , for , The period corresponding to the two frequencies; This represents carrier phase combined observation noise. GF combined observations eliminate the effects of receiver clock bias, satellite clock bias, and tropospheric delay, containing only ionospheric errors and frequency-related observation noise. Pseudorange GF combined... It can be represented as:

[0095] (8)

[0096] In the formula, This is for pseudorange combined observation noise. and They are respectively , Another form of ionospheric delay at two frequencies. To reduce the impact of code pseudorange observation noise, firstly... Perform polynomial fitting to generate pseudo-range GF combination function To filter out the influence of pseudorange noise, the fitting order is... , To obtain the minimum value, The total number of epochs, the next step is to use The discontinuity is used to detect cycle slips.

[0097] (9)

[0098] for abbreviation, For the front Individual calendar Change value, For the front Individual calendar Change value, For the front Individual calendar Change value.

[0099] If two of the following conditions are met, then the current epoch is considered to have a cycle jump. The conditions are as follows:

[0100] (10)

[0101] Based on the above conditions, it can be determined whether a cycle slip exists in the current epoch. For epochs where cycle slips have occurred, they need to be marked as cycle slips and removed in subsequent data processing.

[0102] Step Two: After processing in Step One, carrier phase observation data within the cycle-slip-free period can be obtained, i.e., carrier phase observation data within a continuous arc segment. Next, the carrier phase observations within the continuous arc segment need to be detrended for use in Step Three, the phase flicker index. The calculation of detrending is as follows. Currently, common detrending methods include sliding smoothing, polynomial smoothing (Savitzky-Golay filtering), and wavelet transform. Sliding smoothing relies on the precise determination of the sliding window; windows that are too large or too small will not achieve effective smoothing. While wavelet transform can achieve better smoothing results, its algorithm complexity is high and its applicability is low, which can bring unexpected difficulties in specific programming implementations. Polynomial smoothing, namely SG filtering, can achieve smoothing and denoising simultaneously, effectively filtering out high-frequency noise and showing good adaptability to nonlinear signals. This algorithm has a fast calculation speed, does not require frequency domain transformation, and is suitable for real-time processing scenarios. Although SG filtering also requires the selection of an appropriate window size and polynomial order, these key parameters can be quickly determined through multiple experiments. Therefore, this invention uses SG filtering to perform detrending processing on phase observations within continuous arc segments.

[0103] Polynomial smoothing, or SG filtering, is a filtering algorithm based on local polynomial least squares fitting in the time domain. The idea behind this method is to use carrier phase observations within a sliding window, measured in cycles. Weighted filtering is performed, and the weights are obtained by least-squares fitting of the given higher-order polynomial. The fitting formula is as follows:

[0104] (11)

[0105] In the formula, for Through time Carrier phase observations fitted by a polynomial of order 1; express order polynomial, Indicates the first The fitting coefficients of the order polynomial. Through... The order polynomials in the sliding window Carrier phase observations Perform fitting, for each All can be calculated using equation (11), therefore the following matrix can be constructed:

[0106] (12)

[0107] In the formula, for The carrier phase observation at time [time]. for The fitting error at time step. Equation (12) simplifies to:

[0108] (13)

[0109] in, The measured values ​​correspond to the carrier phase observation matrix in equation (12); Let be the coefficient matrix of the parameters to be estimated; The parameter matrix to be estimated corresponds to the matrix in equation (12). ; Corresponding to the rightmost fitting error matrix in equation (12), i.e. .

[0110] In satisfying the sliding window In this case, the fitting coefficient vector is obtained by solving using the least squares algorithm:

[0111] (14)

[0112] After obtaining the fitting coefficients, they can be calculated using equation (11). The survey found that, for polynomial smoothing, it is recommended to select a sliding window size of [size missing]. or For 1Hz data, choose a 60-second or 90-second window, and it is recommended to choose a polynomial order of 2 to 3.

[0113] Step 3: In Step 1, we acquired observation data based on a 1Hz sampling rate using a standard GNSS receiver, including pseudorange observations, carrier phase observations, and carrier-to-noise ratio. C / No The data was processed, and cycle slip detection was performed on the carrier phase observation data to obtain phase observation values ​​within cycle slip-free periods, i.e., phase observation values ​​within continuous arc segments. In step two, polynomial smoothing was applied to the carrier phase observation values ​​within the continuous arc segments obtained in step one, resulting in detrended carrier phase observation values. Next, the 1Hz carrier-to-noise ratio data output by the ordinary GNSS receiver in step one needs to be used... C / No Calculate the new amplitude scintillation index Based on the detrended carrier phase observations obtained in step two, the phase scintillation index is calculated. .

[0114] (1) New amplitude scintillation index Calculation method

[0115] flicker index It is the most commonly used index to describe ionospheric amplitude scintillation. The index can be calculated using the following formula:

[0116] (15)

[0117] In the formula, The arithmetic mean operator is used. This indicates the signal strength, which is directly proportional to the received signal power. Typically, It includes environmental noise and needs to be detrended. After detrending... It can be represented as :

[0118] (16)

[0119] In the formula, Represents the raw signal strength in decibels (dB); Trend signal strength, expressed in dB, is typically represented by a cutoff frequency of... The original signal strength data is obtained by filtering it with a sixth-order Butterworth filter. For simplicity, it can generally be... The average value over a 60-second span is used as . The difference between the narrowband power (NBP) and the wideband power (WBP) is calculated using the following formula:

[0120] (17)

[0121] (18)

[0122] (19)

[0123] In the formula, and Provide the sampled values ​​of the correlator for 1-kHz in-phase and quadrature phase signals; For navigation message data bits C / A The code cycle number is typically set to 20. For any C / A code period. Typically, the parameter... and Acquired using ionospheric monitoring receivers at frequencies of 50 Hz or higher, the true amplitude scintillation index cannot be calculated using ordinary multi-frequency receivers.

[0124] Although data for calculating the true signal strength cannot be obtained from ordinary GNSS receivers, carrier-to-noise density ratio (CNR) data can be obtained from the RINEX observation files output by ordinary GNSS receivers. C / NoThe value can be calculated using the carrier-to-noise ratio (CNR) to determine the signal-to-noise density ratio (SNR) data. S / No The value is then used to calculate the detrended signal strength using the signal-to-noise ratio data. Finally, equation (15) is used to approximate the true flicker index. The new amplitude scintillation index, namely Index. Research found that, according to statistics compiled by Luo et al., during flickering activity, the index derived from ordinary receivers... The index and the data generated by the ionospheric scintillation monitoring receiver The correlation between indices is typically higher than 0.9. Therefore, for a typical multi-frequency, multi-system GNSS receiver, the new amplitude scintillation index calculated from the carrier-to-noise ratio can be used. As a new indicator for monitoring ionospheric scintillation, its calculation method will be described in detail below.

[0125] First, let's give the carrier-to-noise ratio. C / No The definition of is as follows:

[0126] (20)

[0127] In the formula, C This indicates the minimum signal power required by the receiver; B The difference between the signal strength of a typical observation and the specified minimum signal strength; Antenna gain; L Indicates receiver loss; No Indicates noise density; I Indicates the level of interference; S / No This indicates the signal-to-noise ratio.

[0128] From equation (20), the signal-to-noise ratio can be obtained. S / No The formula for calculation is:

[0129] (twenty one)

[0130] Furthermore, the strength of the detrending signal It can be represented as:

[0131] (twenty two)

[0132] Right now, For the first k Signal strength of each epoch Divide by the signal strength within 1 minute The average value. Among them, This represents the total number of data points within a certain time period, such as 60 seconds. This represents any data point within a specific time period. For raw GNSS data with a 1-second sampling rate, this is typically set... Assuming noise density No If it remains stable for a short period of time, approximating a constant, such as being almost constant within 1 minute, then... No exist k Value at time Approximately within 1 minute No Average value, i.e. Subsequently, the numerator and denominator of equation (22) are simultaneously divided by... Then detrend It can be represented as:

[0133] (twenty three)

[0134] Combining equations (15), (21), and (23), carrier-to-noise ratio data provided by a conventional geodetic GNSS receiver at a sampling rate of 1 Hz can be obtained. C / No Calculate the new amplitude scintillation index This is used to approximate the amplitude scintillation index output by the ionospheric scintillation monitoring receiver. This facilitates low-cost, long-term continuous monitoring of ionospheric scintillation.

[0135] For GNSS observations with a sampling rate of 1 second, the first time interval is calculated using a 60-second time period. The index is then calculated every 60 seconds using a sliding window. The exponent, and time k or the center time of each window as the current. The corresponding time for the index. Research found that, regarding the amplitude flicker index... Generally take To prevent flickering, It is a weak flicker. The flickering intensity is moderate. It exhibits strong flickering. Due to... and The index has a high correlation, therefore it is used When using the index for ionospheric scintillation monitoring, it can be used with... The same index is used to classify flicker intensity.

[0136] (2) Phase flicker index Calculation method

[0137] Phase flicker index It is the most commonly used index to describe ionospheric phase scintillation. By definition, it is the standard deviation of phase fluctuations. For multi-frequency data, the corresponding phase scintillation index can be calculated separately. The calculation formula is:

[0138] (twenty four)

[0139] In the formula, The arithmetic mean operator is used. The detrended carrier phase observations obtained after step two are in radians (rad). During calculation, the carrier phase observations need to be multiplied by... Convert to radians. Calculate using a sliding window. The method of index and the criteria for judging flicker intensity Since the indices are the same, we will not elaborate further.

[0140] Step 4: After the processing in the first three steps, relevant parameters that can be used to calculate receiver tracking error have been obtained. First, the prototype of the receiver tracking error stochastic model constructed by Conker et al. is introduced, and the novel RTES model of this invention is constructed based on the construction idea of ​​this model.

[0141] Conker et al. constructed a stochastic model of receiver tracking error based on a receiver delay-locked loop (DLL) and a phase-locked loop (PLL), known as the RTES model. This model significantly reduces the impact of ionospheric scintillation and improves GPS positioning accuracy under ionospheric scintillation conditions. In the RTES model, the variances of pseudorange and carrier phase observations are respectively derived from the tracking error variances output by the DLL and PLL. and The variance of the DLL tracking error at a given frequency is:

[0142] (25)

[0143] In the formula, This represents the single-sided bandwidth of the DLL, with a value of 0.25Hz. This represents the C / A chip correlator spacing, with a value of 0.04. This is the integration time before detection, with a value of 0.1s; The signal-to-noise ratio at that frequency point can be expressed as the carrier-to-noise ratio. C / No Calculate, the formula is ; This represents the amplitude scintillation index at that frequency. It's important to note that the above formula... is established under the conditions, when At that time, it is necessary to make The value is 0.7.

[0144] The variance of the PLL tracking error at a given frequency can be expressed as:

[0145] (26)

[0146] In the formula, , and These represent the variances of the tracking error caused by thermal noise, phase flicker, and receiver oscillator noise, respectively. This represents the equivalent loop bandwidth of the PLL's one-sided noise, typically taken as 15Hz. This is the integration time before the PLL detector, typically taken as 0.01s; This represents the spectral intensity of the phase noise at 1 Hz on L1; This is the order of the PLL loop, which is usually taken as 3; The natural frequency of the loop is represented by the formula: ; This indicates the slope of the power spectral density of the detrended phase observation, typically within the range of 0.1-25Hz, at that signal frequency. For receiver oscillator noise, the value is taken empirically. .

[0147] It is important to note that and The units are chips and radians, respectively. To maintain consistency with the length units used in GNSS positioning, for... , through Calculation, i.e., the speed of light Divide by code rate Obtain the distance corresponding to a single chip, in meters. Then, in units of chips and Multiplying them together will give you the result in meters. ;for , through Calculation, that is, in radians as a unit Divide by Multiply by the wavelength of the signal Obtain in meters Based on meters and The weight adjustment expression for the constructed RTES model can be expressed as:

[0148] (27)

[0149] In the formula, and These represent the weights of the pseudorange and carrier phase observations at the signal frequency point, respectively. and These are the variances of the pseudorange observations and the carrier phase observations, respectively.

[0150] Next, based on the processing in step three, a new amplitude scintillation index is calculated every minute. and phase flicker index This invention constructs a novel RTES model. First, the model calculated based on data from a standard GNSS receiver... In the exponential substitution equations (25) and (26) The index is used to calculate the variance of the DLL tracking error. and PLL tracking error variance thermal noise variance components .

[0151] For periods where cycle slips occur, cycle slip repair is not performed because carrier phase observations frequently experience cycle slips during ionospheric scintillation and cycle slip repair is difficult. In these cases, only the new amplitude scintillation index can be calculated. Unable to calculate the phase flicker index That is, it can only be based on Index Calculation For the period when cycle slips occur, based on the idea of ​​amplifying the initial variances of pseudorange and phase observations according to a certain ratio when setting them in conventional processing, the proportional relationship between the pseudorange variance and the carrier phase observation variance is calculated under different ionospheric scintillation intensities. Then, the pseudorange variance is amplified according to this proportional relationship to obtain the phase observation variance under the corresponding scintillation intensity.

[0152] For periods when no cycle slips occur, the calculation is performed once per minute. index and The index then yields the DLL tracking error variance once per minute. and PLL tracking error variance thermal noise variance components From equation (26), we can see that... middle Acquired receiver oscillator noise It is a constant, therefore The computational challenge lies in how to calculate the effects caused by phase flicker. .for Tracking error variance caused by mid-phase flicker The parameters required for its calculation formula and It can only be output from ISMR receivers and cannot be calculated directly using the output value of ordinary GNSS receivers. Fortunately, after processing in step three, the phase scintillation index during cycle-slip-free periods can be obtained. Therefore, it can be based on and its distribution pairs Modeling and establishing and The functional relationship between them.

[0153] In step one, at least one year of observation data was obtained using ISMR receivers installed in low-latitude regions and ordinary GNSS receivers with a 1Hz sampling rate. Therefore, the data output from these two receivers was used for analysis and modeling. First, the calculations based on the ISMR receiver output were analyzed. Calculated with the output of a regular GNSS receiver The distribution of these two types of data, considering that GNSS positioning can guarantee good positioning performance under non-scintillation or weak-scintillation conditions, will therefore... Under the conditions Let it be a constant. When hour, Will follow The increase is due to the increase of [something], therefore, a monotonically increasing model is used to [do something]. Perform a fitting. Specifically, the independent variables... The data will be divided into intervals of 0.05 rad, and the corresponding dependent variable... The value is taken as all values ​​within the 0.05 rad interval. The average value. Finally, a fitting model is established using least squares, and a model based on... of Computational model.

[0154] Thus, this invention enables the construction of a novel receiver tracking error stochastic model, namely the novel RTES model, based on ordinary GNSS receiver data. This model... and thermal noise variance components It is possible Index calculation, The variance component of the tracking error caused by phase flicker Then through index and The fitting model is calculated, and index and The index can be calculated using the observations output by a regular GNSS receiver at a sampling rate of 1 Hz.

[0155] The following describes the receiver tracking error stochastic model construction system based on the ionospheric scintillation index provided by the present invention. The receiver tracking error stochastic model construction system based on the ionospheric scintillation index described below can be referred to in correspondence with the receiver tracking error stochastic model construction method based on the ionospheric scintillation index described above.

[0156] Figure 3 This is a schematic diagram of the structure of the receiver tracking error stochastic model construction system based on the ionospheric scintillation index provided in an embodiment of the present invention, as shown below. Figure 3As shown, it includes: a data acquisition module 31, a detection module 32, a processing module 33, a calculation module 34, a first construction module 35, and a second construction module 36, wherein:

[0157] The acquisition module 31 is used to acquire raw GNSS observations at a preset sampling rate using a GNSS receiver at the same location and within the same time period, and to acquire ionospheric observation data using a dedicated ionospheric scintillation monitoring receiver.

[0158] The detection module 32 is used to perform cycle slip detection on the original carrier phase observations in the original GNSS observations based on the TurboEdit algorithm, and output the carrier phase observations during the cycle slip-free period.

[0159] Processing module 33 is used to perform detrending processing on the carrier phase observations in the cycle-slip-free period using a polynomial smoothing method to obtain detrending carrier phase observations.

[0160] The calculation module 34 is used to calculate the new amplitude scintillation index and the phase scintillation index based on the carrier-to-noise ratio data of the preset frequency of the GNSS receiver and the detrended carrier phase observation value.

[0161] The first construction module 35 is used to calculate the variance of pseudorange and carrier phase observations based on the scintillation index output by the dedicated ionospheric scintillation receiver during the cycle slip period, using a classical receiver tracking error stochastic model, to determine the proportional relationship between the variance of pseudorange observations and the variance of carrier phase observations under different scintillation intensities, and to determine the variance of phase observations during the cycle slip period by using the proportional relationship between the variance of pseudorange and phase observations calculated by the new amplitude scintillation index.

[0162] The second construction module 36 is used to establish a scintillation variance calculation formula using the new amplitude scintillation index and the phase scintillation index for cycle-slip-free periods, and to construct a receiver tracking error stochastic model suitable for GNSS receivers, so as to obtain GNSS positioning results under ionospheric scintillation conditions.

[0163] Figure 4 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 4As shown, the electronic device may include: a processor 410, a communication interface 420, a memory 430, and a communication bus 440, wherein the processor 410, the communication interface 420, and the memory 430 communicate with each other through the communication bus 440. The processor 410 can call logical instructions in the memory 430 to execute a method for constructing a random model of receiver tracking error based on the ionospheric scintillation index. This method includes: acquiring raw GNSS observations at a preset sampling rate using a GNSS receiver at the same location and within the same time period; acquiring ionospheric observation data using a dedicated ionospheric scintillation monitoring receiver; performing cycle slip detection on the raw carrier phase observations in the raw GNSS observations based on the TurboEdit algorithm, and outputting the carrier phase observations during the cycle slip-free period; performing detrending processing on the carrier phase observations during the cycle slip-free period using a polynomial smoothing method to obtain the detrended carrier phase observations; and performing detrended processing on the carrier-to-noise ratio data at a preset frequency of the GNSS receiver and the detrended carrier phase observations. For each cycle slip period, based on the scintillation index output by the dedicated ionospheric scintillation receiver, the variances of pseudorange and carrier phase observations are calculated using a classical receiver tracking error stochastic model. The proportional relationship between the pseudorange observation variance and the carrier phase observation variance under different scintillation intensities is determined. Using the proportional relationship between the pseudorange variance calculated by the new amplitude scintillation index and the variances of the pseudorange and phase observations during the cycle slip period, the variance of the phase observations during the cycle slip period is determined. For periods without cycle slips, using the new amplitude scintillation index and the phase scintillation index, a formula for calculating the scintillation variance is established, and a receiver tracking error stochastic model suitable for GNSS receivers is constructed to obtain GNSS positioning results under ionospheric scintillation conditions.

[0164] Furthermore, the logical instructions in the aforementioned memory 430 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0165] On the other hand, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon. When executed by a processor, the computer program implements a method for constructing a random model of receiver tracking error based on the ionospheric scintillation index provided by the above methods. This method includes: acquiring raw GNSS observations at a preset sampling rate using a GNSS receiver at the same location and within the same time period; acquiring ionospheric observation data using a dedicated ionospheric scintillation monitoring receiver; performing cycle slip detection on the raw carrier phase observations in the raw GNSS observations based on the TurboEdit algorithm, and outputting the carrier phase observations within the cycle slip-free period; performing detrending processing on the carrier phase observations within the cycle slip-free period using a polynomial smoothing method to obtain the detrended carrier phase observations; and performing a detrending process based on a preset frequency of the GNSS receiver. Using the carrier-to-noise ratio data and the detrended carrier phase observations, a new amplitude scintillation index and a phase scintillation index are calculated. For cycle-slip periods, based on the scintillation index output by the dedicated ionospheric scintillation receiver, the pseudorange and carrier phase observation variances are calculated using a classical receiver tracking error stochastic model. The proportional relationship between the pseudorange observation variance and the carrier phase observation variance under different scintillation intensities is determined. Using the proportional relationship between the pseudorange variance calculated by the new amplitude scintillation index and the variance of the pseudorange and phase observations during cycle-slip periods, the phase observation variance during cycle-slip periods is determined. For non-cycle-slip periods, using the new amplitude scintillation index and the phase scintillation index, a scintillation variance calculation formula is established, and a receiver tracking error stochastic model suitable for GNSS receivers is constructed to obtain GNSS positioning results under ionospheric scintillation conditions.

[0166] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0167] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0168] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for constructing a random model of receiver tracking error based on the ionospheric scintillation index, characterized in that, include: At the same location and within the same time period, raw GNSS observations were collected using a GNSS receiver at a preset sampling rate, and ionospheric observation data were collected using a dedicated ionospheric scintillation monitoring receiver. Based on the TurboEdit algorithm, cycle slip detection is performed on the original carrier phase observations in the original GNSS observations, and the carrier phase observations during the cycle slip-free period are output. The carrier phase observations during the cycle-slip-free period are detrended using a polynomial smoothing method to obtain the detrended carrier phase observations. Based on the carrier-to-noise ratio data of the preset frequency of the GNSS receiver and the detrended carrier phase observation value, the new amplitude scintillation index and phase scintillation index are calculated. For the cycle slip period, based on the scintillation index output by the dedicated ionospheric scintillation receiver, the variance of pseudorange and carrier phase observations is calculated using a classical receiver tracking error stochastic model. The proportional relationship between the variance of pseudorange observations and the variance of carrier phase observations under different scintillation intensities is determined. The variance of phase observations during the cycle slip period is determined by using the proportional relationship between the pseudorange variance calculated by the new amplitude scintillation index and the variance of pseudorange and phase observations. For cycle-slip-free periods, a scintillation variance calculation formula is established using the new amplitude scintillation index and the phase scintillation index, and a receiver tracking error stochastic model suitable for GNSS receivers is constructed to obtain GNSS positioning results under ionospheric scintillation conditions.

2. The method for constructing a random model of receiver tracking error based on the ionospheric scintillation index according to claim 1, characterized in that, Based on the TurboEdit algorithm, cycle slip detection is performed on the original carrier phase observations in the raw GNSS observations, and the carrier phase observations during cycle slip-free periods are output, including: The TurboEdit algorithm includes the MW combined cycle slip algorithm and the GF combined cycle slip algorithm; The MW combined cycle slip algorithm performs cycle slip detection on the original carrier phase observation values ​​and outputs wide-term cycle slip detection values. The GF combined cycle slip algorithm performs cycle slip detection on the original carrier phase observation values ​​and outputs narrow term cycle slip detection values. The wide-term cycle slip detection values ​​and narrow-term cycle slip detection values ​​of each epoch are screened separately. Carrier phase observation values ​​corresponding to the epochs in which cycle slips occur are removed, and carrier phase observation values ​​in the period without cycle slips are retained.

3. The method for constructing a random model of receiver tracking error based on the ionospheric scintillation index according to claim 1, characterized in that, The carrier phase observations during the cycle-slip-free period are detrended using a polynomial smoothing method to obtain the detrended carrier phase observations, including: Within a sliding window, multiple carrier phase observations are fitted to construct a matrix that includes the fitting coefficients of a polynomial of any order, the fitting error at any time, and the carrier phase observation at any time. The sliding window size and matrix order are determined, and the fitting coefficient vector is obtained by solving the least squares algorithm. The carrier phase observations within the sliding window are weighted and filtered in cycles to obtain the detrended carrier phase observations.

4. The method for constructing a random model of receiver tracking error based on the ionospheric scintillation index according to claim 1, characterized in that, Based on the carrier-to-noise ratio data at a preset frequency of the GNSS receiver and the detrended carrier phase observations, the new amplitude scintillation index and phase scintillation index are calculated, including: Carrier-to-noise ratio (CNR) data is obtained from the RINEX observation files of the GNSS receiver. Signal-to-noise ratio (SNR) data is calculated from the CNR data. Detrended signal strength is calculated from the SNR data. New amplitude scintillation index is obtained based on the detrended signal strength. The detrended carrier phase observations are subjected to mean correlation processing to obtain the phase flicker index.

5. The method for constructing a random model of receiver tracking error based on the ionospheric scintillation index according to claim 1, characterized in that, After calculating the new amplitude scintillation index and phase scintillation index based on the carrier-to-noise ratio data of the preset frequency of the GNSS receiver and the detrended carrier phase observations, the method further includes: The tracking error variance of the delay-locked loop is obtained from the single-sided bandwidth of the delay-locked loop of the GNSS receiver, the spacing between the C / A chip correlators, the pre-detection integration time of the delay-locked loop, the signal-to-noise ratio data, and the amplitude scintillation index. The phase-locked loop tracking error variance is obtained from the equivalent loop bandwidth of the phase-locked loop single-sided noise, the phase-locked loop pre-detection integration time, the signal-to-noise ratio data, the amplitude scintillation index, the spectral intensity of the phase noise at the preset frequency, the phase-locked loop order, the loop natural frequency, the slope of the power spectral density of the detrended phase observation value within the preset frequency range around the signal frequency point, and the oscillator noise of the GNSS receiver. The pseudorange observation weight and the carrier phase observation weight are obtained by calculating the variance of the tracking error of the delay-locked loop and the reciprocal of the variance of the tracking error of the phase-locked loop, respectively. Replace the amplitude scintillation index in the calculation of the tracking error variance of the delay-locked loop and the tracking error variance of the phase-locked loop with a new amplitude scintillation index to determine the new tracking error variance of the delay-locked loop and the thermal noise variance component in the tracking error variance of the phase-locked loop.

6. The method for constructing a random model of receiver tracking error based on the ionospheric scintillation index according to claim 5, characterized in that, For the cycle slip period, based on the scintillation index output by the dedicated ionospheric scintillation receiver, the variances of pseudorange and carrier phase observations are calculated using a classical receiver tracking error stochastic model. The proportional relationship between the pseudorange observation variance and the carrier phase observation variance under different scintillation intensities is determined. Using the proportional relationship between the pseudorange variance calculated by the new amplitude scintillation index during the cycle slip period and the variances of the pseudorange and phase observations, the variance of the phase observations during the cycle slip period is determined, including: Based on the scintillation index output by a dedicated ionospheric scintillation receiver, the variances of pseudorange and carrier phase observations are calculated using a classical receiver tracking error stochastic model. Under different scintillation intensities, the proportional relationship between the variance of the pseudorange observations and the variance of the carrier phase observations was determined. The variance of the pseudorange during the cycle slip period is calculated using the new amplitude scintillation index, and the proportional relationship between the pseudorange and the variance of the phase observation is used to obtain the variance of the phase observation during the cycle slip period by multiplying the pseudorange variance by the proportional relationship.

7. The method for constructing a random model of receiver tracking error based on the ionospheric scintillation index according to claim 5, characterized in that, For cycle-slip-free periods, a scintillation variance calculation formula is established using the new amplitude scintillation index and the phase scintillation index. This constructs a stochastic model for receiver tracking error suitable for GNSS receivers, yielding GNSS positioning results under ionospheric scintillation conditions, including: The phase-locked loop tracking error variance includes the thermal noise variance component, the phase flicker noise variance component, and the receiver oscillator noise variance component, wherein the receiver oscillator noise variance component is a constant. A formula for calculating the scintillation variance of the phase scintillation noise variance component is established based on the phase scintillation index, thereby constructing a random model of receiver tracking error suitable for GNSS receivers; Error estimation is performed using the receiver tracking error stochastic model to obtain GNSS positioning results under ionospheric scintillation conditions.

8. A system for constructing a random model of receiver tracking error based on the ionospheric scintillation index, characterized in that, include: The acquisition module is used to acquire raw GNSS observations at a preset sampling rate using a GNSS receiver at the same location and within the same time period, and to acquire ionospheric observation data using a dedicated ionospheric scintillation monitoring receiver. The detection module is used to perform cycle slip detection on the original carrier phase observations in the original GNSS observations based on the TurboEdit algorithm, and output the carrier phase observations during the cycle slip-free period. The processing module is used to perform detrending processing on the carrier phase observations during the cycle-slip-free period using a polynomial smoothing method to obtain the detrending carrier phase observations. The calculation module is used to calculate the new amplitude scintillation index and phase scintillation index based on the carrier-to-noise ratio data of the preset frequency of the GNSS receiver and the detrended carrier phase observation value; The first construction module is used to calculate the variance of pseudorange and carrier phase observations based on the scintillation index output by the dedicated ionospheric scintillation receiver during the cycle slip period using a classical receiver tracking error stochastic model. It determines the proportional relationship between the variance of pseudorange observations and the variance of carrier phase observations under different scintillation intensities. It then uses the proportional relationship between the variance of pseudorange during the cycle slip period calculated by the new amplitude scintillation index and the variance of pseudorange and phase observations to determine the variance of phase observations during the cycle slip period. The second construction module is used to establish a scintillation variance calculation formula using the new amplitude scintillation index and the phase scintillation index for cycle-slip-free periods, and to construct a receiver tracking error stochastic model suitable for GNSS receivers, so as to obtain GNSS positioning results under ionospheric scintillation conditions.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the receiver tracking error stochastic model construction method based on the ionospheric scintillation index as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the receiver tracking error stochastic model construction method based on the ionospheric scintillation index as described in any one of claims 1 to 7.

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