Random model optimization method based on GNSS signal anti-multipath performance difference

Abstract

The present application relates to the field of satellite navigation and positioning technology, and particularly relates to a random model optimization method based on GNSS signal anti-multipath performance difference, comprising the following steps: S1, observation data collection and environment division: collecting multi-frequency GNSS data; S2, multipath error epoch-to-epoch variation feature extraction: extracting error variation identification difference frequency points; S3, error factor determination and proportion construction: backstepping error intensity, establishing frequency point proportion relationship; S4, fusion error factor height angle random model construction: introducing factor adjustment weight; S5, positioning solution accuracy analysis and model verification: comparing positioning results to evaluate model effect; the present application, by fusing the anti-multipath performance difference of different GNSS frequency points, constructs a differentiated weighted random model, effectively improves the positioning accuracy in a strong multipath environment and takes into account the model adaptability.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation and positioning technology, and in particular to a stochastic model optimization method based on the multipath performance differences of GNSS signals. Background Technology

[0002] With the widespread application of Global Navigation Satellite Systems (GNSS) in fields such as marine surveying, autonomous driving, and aviation navigation, the issue of positioning accuracy has received high attention. Multipath error is a key factor affecting the accuracy of GNSS precise positioning, especially in strong reflection environments such as oceans and urban canyons. In order to improve the solution accuracy, researchers generally adopt the non-difference non-combination precise point positioning (PPP) method and introduce an elevation angle stochastic model in the weight modeling to suppress the error interference of low elevation angle observations. However, with the widespread access of GNSS multi-band signals, a single elevation angle weight model is no longer able to cover the error distribution changes caused by the differences in anti-interference performance between frequency points.

[0003] Existing PPP stochastic modeling methods generally fail to distinguish the differences in multipath resistance of different frequency signals, leading to significant errors introduced by some weaker frequency points in strong multipath environments, thereby reducing the overall accuracy of the solution. In addition, traditional weight adjustment mechanisms based on C / N0, elevation angle, or ambiguity residuals are difficult to take into account both frequency specificity and error source structure, and lack modeling and response strategies for the evolution trend of multipath errors. Therefore, in PPP solution scenarios that integrate multi-frequency observations, there is an urgent need for a dynamic error control mechanism oriented towards frequency differences to improve the model's adaptability to complex error environments. Summary of the Invention

[0004] This invention provides a stochastic model optimization method based on the multipath performance differences of GNSS signals. By constructing a frequency point difference error factor and introducing it into the elevation angle stochastic model for weighted correction, it achieves effective suppression of inferior frequency point observations in strong multipath environments, thereby significantly improving the positioning accuracy in the plane direction and ensuring the stable applicability of the model in different multipath scenarios.

[0005] A stochastic model optimization method based on the multipath resistance performance differences of GNSS signals includes the following steps:

[0006] S1. Observational data acquisition and environmental classification: In marine and terrestrial environments, stations using the same type of receiver and antenna are deployed to collect GNSS observation data, including GPS L1, L2, L5 signals, Galileo E1, E5a, E5b signals, BDS2 B1I, B2I, B3I signals, and BDS3 B1C, B3I signals. The marine environment is regarded as a strong multipath environment and the terrestrial environment is regarded as a weak multipath environment, so as to establish a comparative observation dataset under different multipath influence scenarios.

[0007] S2, Multipath Error Inter-Epoch Variation Feature Extraction: In the observation data segment where cycle slip does not occur, a multipath combination is constructed based on the original code and phase observation values. The multipath error variation of different frequency signals is extracted by the inter-epoch single difference method. The stability differences of each frequency signal in strong and weak multipath environments are compared by using different auxiliary frequency combination methods. In this way, the frequency points that exhibit error fluctuations in strong multipath environments are identified, and it is judged that their anti-multipath performance is poor.

[0008] S3, Error Factor Determination and Proportion Construction: Based on the code multipath combination fluctuation characteristics extracted in a strong multipath environment, the phase multipath error fluctuation intensity related to the frequency signal is deduced, and the relative error intensity ratio is established using GPS L5, Galileo E5a, BDS2 B2I and BDS3 B1C as representative signals.

[0009] S4, Construction of Elevation Angle Random Model for Fusing Error Factors: Based on the elevation angle random model, an error amplification factor for signals with poor multipath performance is introduced, and its weight in the positioning solution model is controlled by the amplification factor. This constructs an elevation angle random model for fusing signal frequency points to resist multipath performance differences, which is used to dynamically adjust the observation noise level of different signals in the solution.

[0010] S5, Positioning accuracy analysis and model validity verification: Using the unoptimized and optimized elevation angle stochastic models respectively, single-point positioning calculations were performed on GNSS observation data under a strong multipath environment. By comparing the root mean square values ​​of positioning errors in the E, N, and U directions, the improvement effect of the optimized model on horizontal accuracy was evaluated.

[0011] Optionally, the multipath error epoch variation feature extraction in S2 includes:

[0012] S21, Observation Model Construction: Based on the composition of GNSS observation data, a code observation model and a carrier observation model are established at frequency i to express the influence paths of various error components in the observation data, represented as:

[0013] P i =ρ+c(δt) r-δt s )+I i +T+M i +d r,i +d s,i +ε(P i );

[0014] L i =ρ+c(δt) r -δt s )-I i +T+m i +b r,1 +b s,1 +λ i N i +ε(L i );

[0015] Where P and L represent code observations and carrier phase observations, respectively, i represents different frequencies, ρ represents the geometric distance from the satellite to the station antenna, c is the speed of light in vacuum, and δt is the velocity of light. r and δt s I represents the clock difference between the receiver clock and the satellite clock, respectively. i Indicates ionospheric delay, T is tropospheric delay, and M is tropospheric delay. i and m i These represent code multipath and carrier phase multipath, respectively, d r,i and d s,i These represent the frequency-dependent code hardware delays at the receiver and satellite ends, respectively, b r,i and b s,i λ represents the frequency-dependent phase hardware delay at the receiver and satellite ends, respectively. i Represents frequency f i The corresponding wavelength, N i For carrier phase integer ambiguity, ε(P) i ) and ε(L i These represent the observation noise for the code and carrier phase, respectively.

[0016] S22, Code multipath combination construction: Construct the code multipath combination term between the main frequency i and the auxiliary frequency j, and then extract the frequency-related observation error term, represented as:

[0017]

[0018] Among them, MP i,j These are code multipath observations at frequency i;

[0019] S23, Multi-frequency combination term expansion analysis: The combination terms are algebraically expanded to reveal the weights and propagation paths of each error component, distinguishing between phase multipath error, observation noise term, and ambiguity term, expressed as:

[0020]

[0021]

[0022] S24, Multi-path combination mean removal: Within a cycle-slip-free arc segment, extract and remove the average value of the combination terms to obtain the true trend of the combination's change within that arc segment, expressed as:

[0023]

[0024] S25, Extraction of inter-epoch change trends: Perform epoch differencing on the combined terms after removing the average value, extract its gradient over continuous time, and construct an error change sequence, represented as:

[0025]

[0026] Optionally, the error term of the inter-epoch change in S25 is expanded as follows:

[0027]

[0028] Optionally, the error factor determination and scale construction in S3 include:

[0029] S31, Multipath Combination Standard Deviation Extraction: Extraction of code multipath combination terms for each frequency signal. Perform epoch differencing and calculate its standard deviation over the cycle-slip-free arc segment, denoted as .

[0030] S32, Phase multipath error standard deviation inverse calculation: Based on the multipath propagation model and frequency combination coefficients, Convert to phase multipath error standard deviation Represented as:

[0031]

[0032] in, It is the abnormal fluctuation of ΔMP ij standard deviation Yes, Δm j standard deviation It is Δm j The corresponding coefficient.

[0033] Optionally, the elevation angle stochastic model construction of the fusion error factor in S4 includes:

[0034] S41, Elevation Angle Model Construction: A sinusoidal function stochastic elevation angle model is established based on the satellite elevation angle to describe the variation trend of observation noise with elevation angle, expressed as:

[0035]

[0036] Where m and n are constants, θ e For the satellite elevation angle, σ(θ) e ) represents the standard deviation of the observed noise;

[0037] S42, Introducing a frequency point error factor for weighted correction: Based on the constructed sinusoidal function elevation angle stochastic model, a frequency point differential error factor is introduced. Construct a frequency-dependent random error model, expressed as:

[0038]

[0039] Optionally, the frequency point differentiation error factor By using the phase multipath error standard deviation σ(Δm) i The result is calculated using the set magnification factor K, and expressed as:

[0040] EF i =σ(Δm) i )·K.

[0041] Optionally, the positioning solution accuracy analysis and model validity verification in S5 include:

[0042] S51, Model Replacement and Solution Comparison: Based on DYLS station data, non-difference, non-combination PPP solution processing was performed using the sinusoidal function elevation angle stochastic model before and after correction.

[0043] S52, RMS Error Assessment: Set multiple elevation angle thresholds, statistically analyze the positioning RMS errors in the E, N, and U directions, and verify the improvement effect of the optimized model on planar positioning accuracy in a strong multipath environment.

[0044] The beneficial effects of this invention are:

[0045] This invention combines the observational fluctuation differences of GNSS signals at different frequencies under strong and weak multipath environments, and extracts the error variation using multi-frequency observation combinations. This effectively identifies frequency signals with poor multipath resistance. Furthermore, by constructing a phase multipath error standard deviation back-calculation model, the difference in frequency error intensity is extracted and uniformly normalized to form a frequency difference factor, thus realizing a systematic correction and frequency fusion expansion of the traditional elevation angle stochastic model.

[0046] This invention significantly reduces the adverse effects of frequency signals with weak multipath resistance on positioning accuracy by introducing frequency error factors into a stochastic model and participating in precise point positioning (PPP) calculation. It effectively improves RMS positioning accuracy in the E and N directions in typical marine environments. At the same time, the model maintains good compatibility in weak multipath environments, verifying its practicality and robustness in GNSS accuracy optimization in multiple scenarios. Attached Figure Description

[0047] 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 only for this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0048] Figure 1 This is a schematic diagram of the allocation method according to an embodiment of the present invention;

[0049] Figure 2 This is a schematic diagram showing the calculations obtained by using different auxiliary frequencies at the DYLL and DYLS stations in an embodiment of the present invention.

[0050] Figure 3 This is a schematic diagram illustrating the standard deviation of each satellite in different GNSS systems calculated using different auxiliary frequencies at the DYLL and DYLS stations, according to an embodiment of the present invention.

[0051] Figure 4 This is a schematic diagram of the standard deviation of a signal with weak resistance to multipath propagation, calculated based on the standard deviation of abnormal fluctuations, according to an embodiment of the present invention.

[0052] Figure 5 This is a schematic diagram illustrating the standard deviation of the fluctuation term of C / N0 for different signals in an embodiment of the present invention.

[0053] Figure 6 This is a schematic diagram of the C / N0 of different signals of the GPS, Galileo, BDS2, and BDS3 systems in an embodiment of the present invention;

[0054] Figure 7 This is a schematic diagram of the root mean square error of the DYLS station UC-PPP positioning results in the E, N, and U directions, according to an embodiment of the present invention. Detailed Implementation

[0055] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. Those skilled in the art may employ other alternative methods to implement some well-known technologies; moreover, the accompanying drawings are only for more specific description of the embodiments and are not intended to specifically limit the present invention.

[0056] like Figures 1-7 As shown, the stochastic model optimization method based on the multipath resistance performance differences of GNSS signals includes the following steps:

[0057] 1.1 Methods for Multipath Variation Extraction and Multipath Resistance Comparison:

[0058] Since multipath error is a non-zero mean error, changes in the surrounding environment of the station and the spatial position of the satellite will alter the signal reflection conditions, making it impossible to directly extract the absolute value of multipath error from the raw observation data. This study investigates multipath characteristics by extracting the inter-epoch changes of multipath data from the raw observations based on multipath combinations, which can reflect the stability of multipath. Both code and phase observations are affected by multipath effects, but the impact on code observations is much greater than that on phase multipath. The raw observation equations for code and phase containing multipath errors can be expressed as Equations 1 and 2, respectively:

[0059] P i =ρ+c(δt) r -δt s )+I i +T+M i +d r,i +d s,i +ε(P i (1)

[0060] L i =ρ+c(δt) r -δt s )-I i +T+m i +b r,1 +b s,1 +λ i N i +ε(L i (2)

[0061] Where P and L represent code observation and carrier phase observation, respectively, both in meters; the subscript i indicates different frequencies; ρ represents the geometric distance from the satellite to the station antenna; c is the speed of light in vacuum; and δt is the distance from the satellite to the station antenna. r and δt s These represent the clock difference between the receiver clock and the satellite clock, respectively, in seconds. i The delay represents ionospheric delay, T represents tropospheric delay, and the unit is meters (M). i and m i These represent code multipath and carrier phase multipath, respectively, in meters (d). r,i and d s,i These are the frequency-dependent code hardware delays (UCD, uncalibrated code delay) at the receiver and satellite ends, respectively. r,i and bs,i These are the uncalibrated phase delays (UPD) at the receiver and satellite, respectively, which are frequency-dependent. i Represents frequency f i The corresponding wavelength, in meters; N i The carrier phase integer ambiguity is expressed in cycles; ε(P) i ) and ε(L i ) represent the observation noise of the code and carrier phase, respectively. The code multipath combination is shown in Equation 3:

[0062]

[0063] MP i,j This is the code multipath observation at frequency i. Frequency j is also used in this combination, primarily to eliminate the influence of ionospheric delay on the multipath observations during the process. Frequency i will be referred to as the primary frequency, and frequency j as the auxiliary frequency. Using Equation 3, the geometric distance ρ from the satellite to the station antenna and the receiver clock bias δt are... r Satellite clock bias δt s Both the tropospheric delay T and the ionospheric delay I will be eliminated. Therefore, Equation 3 can be further expressed as shown in Equation 4:

[0064]

[0065] Among them B i,j Represented as:

[0066]

[0067] In Equation 5, the code hardware delay d at the receiver end and the satellite end r,i and d s,i and phase hardware delay b r,i and b s,i It exhibits short-term stability. Without cycle slip, the integer ambiguity N... i It will also be a constant. Therefore, B on the arc segment without cycle slip. i,j It is relatively stable and can be considered a constant. Typically, MP... i,j Subtract MP on the arc without cycle jump i,j The average value can be used to eliminate B. i,j However, MP can only be extracted after a complete cycle-slip-free arc segment has been determined. i,j It can only be dealt with afterward, as shown in Equation 6.

[0068]

[0069] MP ij,varThis represents the changing trend of multiple paths across the entire cycle-skip-free arc segment. To extract multiple paths in real time and understand their stability, this study employs an inter-epoch single-difference method to eliminate B... i The effects are shown in Equations 7 and 8.

[0070]

[0071] Equation 7 uses code observations and phase observations at frequency i and phase observations at frequency j to extract epoch-time variations in the code multipath. When the receiver can observe three-frequency data, the phase observation data at frequency j (auxiliary frequency) can be replaced with phase observations at other frequencies. As shown in Equation 8, when frequency j is replaced with frequency k, the frequency i-related... Δε(L i ) t and Δε(P) i ) t It will not change; the coefficient becomes Meanwhile, the epoch difference of the phase multipath and the epoch difference of the phase observation error corresponding to the auxiliary frequency become respectively... and Δε(L k ) t In the same observation environment, and Related to frequency i and Δε(P) i ) t Since they remain unchanged and have no coefficients, their two parameters are inversely related. and The effects are the same. and Related to frequency i and Δε(L i ) t Although they are the same, their corresponding coefficients have changed, so under the influence of the coefficients, they have different effects on... and The effects are not consistent. and In the middle, the Δm corresponding to auxiliary frequencies i and j t and Δε(L) t And their coefficients have all changed, so they affect and The impact is also inconsistent.

[0072] There are four main types of receiver noise: background radiated noise, thermal noise, equipment noise, and external interference. Among these, phase multipath error (m) is a significant factor. iExternal interference, ε(L), is mainly the sum of background radiated noise, thermal noise, and equipment noise. Background radiated noise is primarily composed of astronomical noise and atmospheric noise. If the two receivers are spatially close and there is no significant solar activity or weather change during the observation period, the background noise is almost identical and relatively stable. Thermal noise is mainly affected by temperature. When the ambient temperatures of the two receivers are similar, the magnitude and stability of the thermal noise are not significantly different. Using the same type of antenna and receiver, with identical hardware architecture and signal handling methods, the magnitude and stability of equipment noise will not differ significantly. Therefore, when two stations using the same type of receiver and antenna are spatially close, ε(L) will not differ significantly. In Section 2.1, the phase observation noise of the receivers used was further extracted based on the zero-baseline observations using the strategy shown in Equation 9.

[0073]

[0074] In Equation 9, Δ represents the time difference, A and B represent the two receivers forming the zero baseline, and sat1 and sat2 represent two different satellites. This method can eliminate parameters other than phase observation error in Equation 2. E(ΔL) DD ) and D(ΔL DD ) represent ΔL DD Expectation and variance, standard deviation of phase observation error Based on the phase observation error extraction method described above, it can be proven in the experiment in Section 2.1 that Δε(L) t The magnitude is very small, and even after amplification by coefficients, it will not have a significant impact on ΔMP.

[0075] Observations were conducted simultaneously using the same receiver and antenna in both strong and weak multipath environments. Data from both environments were used to extract the data using methods from Equations 7 and 8, respectively. and Based on the above analysis, Δε(L) t The magnitude is very small, and the Δε(L) between the two stations is... t The differences between them are also very small. Therefore, regardless of whether it is a strong or weak multipath environment, Δε(L) t right and The impacts are almost identical and very small. In a strong multipath environment... and The differences between them are large in a weak multipath environment and small in a strong multipath environment. According to the error propagation law, it can be inferred that in a strong multipath environment... and The one with the abnormally large fluctuation range is caused by Or it could be the Δm corresponding to its auxiliary frequency.t The abnormal fluctuations are caused by the coefficients, which further amplify these abnormal fluctuations, thus affecting the fluctuations of ΔMP. Therefore, compared to strong and weak multipath environments... and The differences can reflect the stability of signals at different frequencies, which is the method used in this study to reflect the signal's resistance to multipath propagation through raw observation data.

[0076] While the Difference Ionosphere-Free (DIF) method can extract the phase multipath variation characteristics, it cannot extract the phase multipath at a single frequency. As shown in Equation 10, the DIF combination is constructed by subtracting two ionosphere-free combinations based on three-frequency observation data. The DIF(L1,L2,L3) also includes ambiguity and phase hardware delay, and the average value of DIF(L1,L2,L3) on the cycle-slip-free arc segment needs to be subtracted. The phase multipath observations are shown in Equation 11. They contain three phase multipaths at different frequencies, making it difficult to separate them to compare the anti-multipath performance of signals at different frequencies.

[0077] DIF(L1,L2,L3)=IF(L1,L2)-IF(L1,L3) (10)

[0078]

[0079] 1.2 Extraction of C / N0 fluctuation term affected by multipath:

[0080] C / N0 represents the ratio between the power of the carrier signal and the power spectral density of the noise within a 1Hz bandwidth. When the satellite signal is affected by multipath error, C / N0 can be written in the following form:

[0081]

[0082] f represents the signal frequency. It is nominal C / N0. This indicates the portion affected by multipath propagation. Due to multipath propagation, C / N0 i Will Asynchronous fluctuations occur nearby. B represents another component caused by signal propagation, primarily due to non-line-of-sight (NLOS) signals. The difference is that bias B may not exist; if this bias is absent, B can be ignored. The experiments in this study were primarily conducted at sea, where there was no signal obstruction, so the influence of B will not be considered further. i This represents random error. According to Equation 12, It can be written in the following form:

[0083]

[0084] In theory, The signal is affected by variations in the satellite signal transmitter's power output, the receiving system (including the preamplifier, antenna, and receiver), the receiver antenna gain, and signal spread. The receiver antenna gain is related to the elevation angle, so C / N0 can be observed. i There is a correlation with the elevation angle. In an ideal environment with constant satellite transmit power, C / N0... i It is minimally affected by multipath propagation, i.e. If it is very small, then C / N0 i Mainly composed of The composition is related to and stable with the elevation angle. If GNSS observations are subject to strong multipath interference, Will affect C / N0 i This has a significant impact, leading to C / N0 i Will Asynchronous fluctuations occurred nearby, so C / N0 i The stability of the C / N0 ratio, to some extent, represents the stability of multipath signals. In this study, we performed low-order polynomial fitting on the C / N0 data of different observed signals and removed the trend term. The stability of the remaining fluctuation term can reflect the multipath stability of signals at different frequencies. Therefore, by comparing the C / N0 ratios of different frequency signals... i The fluctuation term can be used to understand the multipath resistance of different signals.

[0085] 2.1 Analysis of the signal's resistance to multipath errors based on inter-epoch variation characteristics:

[0086] The methods described in Section 1.1 will be used to compare and analyze the differences in multipath resistance performance of different signals. ΔMP was extracted using Equations 7 and 8 based on the available signal types in the observed data. Since the receiver only observed two signals from the GLONASS system, it could not meet the requirement of at least three frequency observations for Equations 7 and 8, thus preventing the analysis of the GLONASS system's signal multipath resistance performance.

[0087] Based on the analysis in Section 1.1, when two stations using the same type of antenna and receiver are spatially close, the difference in ε(L) is not significant. Using the method shown in Equation 9 to extract ε(L) for different signals, except for the larger ε(L) of the B1I and B3I signals from the BDS2GEO satellite, the ε(L) of the GPS, Galileo, and BDS3 signals are mostly in the sub-millimeter range. These two conclusions together explain that the difference in ε(L) between the DYLL and DYLS stations is small, and also of a small order of magnitude.

[0088] Based on equations 7 and 8, ΔMP during the observation period of the G01 satellite was obtained using different auxiliary frequencies j and k. ij With ΔMP ik ,like Figure 2 As shown in the diagram. The red numbers in the subscript ΔMP represent the primary frequency i, and the following black numbers represent the auxiliary frequencies. i, j, and k represent the corresponding frequencies. From... Figure 2 It can be seen that, using different auxiliary frequencies, the ΔMP obtained at the DYLL station... ij With ΔMP ik Only minor differences exist. Since it has already been proven that the magnitude of ε(L) is small for both the DYLL and DYLS stations, and the difference between ε(L) between the two stations is also small, considering σ(ε(L)) and its corresponding coefficients, according to the error propagation law, the ΔMP of the DYLL station... ij With ΔMP ik The slight difference between them is reasonable. Theoretically, at the DYLS station, Δε(L) should not lead to ΔMP. ij With ΔMP ik There are obvious differences between them. However, in Figure 2 In the middle, the ΔMP of the DYLS station ij With ΔMP ik However, there are significant differences, far exceeding the impact of the phase observation error ε(L) and its corresponding coefficient. According to the comparison method described in Section 1.1, for the same type of receiver and antenna, if ΔMP in a strong multipath environment… ij With ΔMP ik When the differences between them are significantly different from those in a weak multipath environment, if the influence of Δε(L) is excluded, it can be inferred that the differences between them are caused by Δm. Therefore... Figure 2 This means that the variation amplitude of phase multipath m of different frequency signals in a strong multipath environment is quite large, which also means that the anti-multipath performance of different frequency signals is different.

[0089] because Figure 2 Only the differences in ΔMP of the G01 satellite were shown, which is not universally applicable. Therefore, we selected 500 epochal data points near the maximum elevation angle of all visible satellites in each system to calculate the standard deviation of ΔMP, such as... Figure 3 As shown. Because the distance between the experimental vessel and the land-based reference station was not very far in this experiment, the difference in satellite elevation angle observed by the DYLL and DYLS stations was very small. Figure 3 The distinction is no longer made. It can be seen that the ΔMP calculated by each satellite in different systems at the DYLL station... ij With ΔMP ik The standard deviations did not differ significantly, but the ΔMP at the DYLS station was different. ijWith ΔMP ik There are significant differences. All satellites within the same system exhibit the same characteristics, indicating that these differences are not due to the unique characteristics of any single satellite within the system, but rather are related to the signal type of the system. According to... Figure 3 ΔMP of satellites in various systems ij With ΔMP ik The difference characteristics will ΔMP ij With ΔMP ik The coefficient of the one with the largest variation is marked in blue, and the marked ΔMP is considered to be... i The stability of the main frequency i or the auxiliary frequency corresponding to Δm is poor in a strong multipath environment.

[0090] Figure 2 In section 3, for ΔMP2 of the GPS system, compared with the DYLL station, the ΔMP2 extracted using the DYLS station data is... 23 The magnitude of the change is much greater than ΔMP 21 We can then suspect that this huge difference is caused by Δm corresponding to frequencies f2 or f3. For ΔMP3 in the GPS system, compared to the DYLL station, the ΔMP3 extracted using DYLS station data... 32 The magnitude of the change is much greater than ΔMP 31 Therefore, it is suspected that the difference between the two is caused by Δm corresponding to frequencies f2 or f3. For ΔMP1 of the GPS system, compared with the DYLL station, the ΔMP1 extracted using DYLS station data... 13 The magnitude of the change is also greater than ΔMP 12 Therefore, it is suspected that the difference between the two is caused by Δm corresponding to frequencies f1 or f3. 13 With ΔMP 12 The variation amplitudes are relatively small, mainly because their corresponding coefficients a and b are small, resulting in a small amplification effect on the abnormal fluctuations of Δm. Based on all the evidence above, when frequency f3 is involved in the calculation of ΔMP, ΔMP in a strong multipath environment... ij and ΔMP ik Since there are differences, it can be inferred that these three pairs of ΔMP are caused by Δm3 corresponding to frequency f3 (L5 signal). ij and ΔMP ik The difference in amplitude between them.

[0091] For other positioning systems, according to Figure 3 Based on the above reasoning process, the f2 frequency (E5a signal) of the Galileo system, the f3 frequency (B2I signal) of the BDS2 system, and the f3 frequency (B1C signal) of the BDS3 system are considered to cause ΔMP in a strong multipath environment. ij With ΔMPik There are significant differences between them, but these differences do not exist in weak multipath environments. In other words, these signals have relatively weaker multipath resistance in their respective systems compared to other signals. Unfortunately, the B3I signal of BDS3 was not received at the DYLL station, so only ΔMP could be extracted at the DYLL station. 12 and ΔMP 21 However, based on the B3I signal observed at the DYLL station and the B3I signals observed at the DYLS station for BDS2 and BDS3, it can be inferred that this signal does not cause abnormal fluctuations in ΔMP. Therefore, the missing data will not significantly affect the above conclusions.

[0092] according to Figure 2 , 3 It can be observed that at the DYLS station, if the poor multipath resistance of the j-frequency signal has been determined, then ΔMP ij It will exhibit abnormal fluctuations, and the ΔMP of the j-frequency signal was not used during extraction. ik It is extremely small and very smooth. Therefore, ΔMP can be achieved. ik The characteristic is ΔMP i Normal variation characteristics at DYLS stations, such as ΔMP in GPS systems. 12 and ΔMP 21 ΔMP of the Galileo system 13 and ΔMP 31 The above analysis shows that ΔMP ij Relative to ΔMP ik The large fluctuations are mainly due to the weak resistance to multipath propagation by f. j Δm of the signal j Caused by this, then relative to the extremely small and smooth ΔMP ik We believe Δm j The standard deviation, after being amplified by a coefficient, is approximately equal to the abnormal fluctuation ΔMP. ij The standard deviation. Therefore, the abnormal fluctuations ΔMP at the DYLS station. ij Standard deviation divided by Δm j The preceding coefficients can be used to approximate Δm. j The standard deviation is shown in Equation 14:

[0093]

[0094] in It is the abnormal fluctuation of ΔMP ij standard deviation Yes, Δm j standard deviation It is Δm jThe corresponding coefficients and their relationships can be found using equations 7 and 8. For example, Figure 2 , 3 In the GPS system, ΔMP 23 There are abnormal fluctuations, and it has been deduced that the f3 frequency is a signal with weak multipath resistance, and its Δm3 is also a cause of ΔMP. 23 The main reason for abnormal fluctuations, therefore With ΔMP 23 The corresponding coefficient b is 22.5106. According to Equation 14, the calculation result is as follows: Figure 4 As shown.

[0095] from Figure 4 It can be seen that all observable satellites in the GPS system and Almost overlapping The slight deviation from them is mainly due to ΔMP 31 The coefficients a and b with ΔMP 13 and ΔMP 23 The corresponding coefficients a and b have opposite signs. Even if ΔMP 31 The medium is also affected by Δm3, but no abnormal fluctuations were observed. This is partly because its coefficients a and b are relatively small, and partly because ΔMP... 31 The coefficients and ΔMP 13 and ΔMP 23 The corresponding coefficients a and b have opposite signs. Utilizing the anomalous change in ΔMP... 32 ΔMP 13 and ΔMP 23 The standard deviation is obtained through reverse derivation. The near-identical results further demonstrate that Δm3 does indeed cause ΔMP. ij With ΔMP ik The main reason for the significant differences is that the f3 frequency (L5 signal) has poor multipath resistance. Similarly, the σ values ​​of the E5a signals of each Galileo satellite calculated using the method described above... Δ m2, σ of B2I signals of each BDS2 satellite Δ B1C signals of each satellite in m3 and BDS3 They are almost identical, such as Figure 4 As shown, these signals also demonstrate that Δm corresponds to these signals and indeed causes ΔMP within each system. ij and ΔMP ik The main factors also indicate that these signals have poor multipath resistance within their respective systems. It is worth noting that when extracting the multipath error MP using the code multipath combination shown in Equation 4, it is generally assumed that the smaller the coefficients, the smaller the introduced phase multipath error m and phase observation error ε(L). For ΔMP with similar coefficients...ij and ΔMP ik (e.g., ΔMP of GPS system) 12 With ΔMP 13 In a strong multipath environment, even with relatively small coefficients, the MP value can still deviate from its true value due to the signal's resistance to multipath propagation. Therefore, when studying code multipath characteristics in such a strong multipath environment, combinations with smaller coefficients may not actually be the best choice.

[0096] Figure 3 The coefficients marked in blue in China and Africa correspond to ΔMP ij The signals were not significantly affected by signals with weak multipath resistance, thus accurately reflecting the true characteristics of code multipath variation on the sea surface. The code multipath variation at the DYLS station was relatively stable, while that at the DYLL station was more drastic. Notably, this characteristic was observed in the code multipath variations of all satellite systems in this experiment. Analysis suggests this variation is caused by the different signal reflection types at the two stations. The water surface has a high reflection coefficient, and the wave height during the observation period was approximately 1 meter, classifying it as a light wave. Therefore, the signal reflection type at the DYLS station was almost specular reflection. The DYLL station was surrounded by rough concrete material with a very low reflection coefficient, resulting in diffuse reflection. Specular reflection offers greater determinism, with smaller phase and amplitude fluctuations in the reflected electromagnetic waves. Diffuse reflection signals are characterized by phase incoherence, large amplitude vibrations, and high directional uncertainty. Furthermore, diffuse reflection occurs over a larger reflective surface, meaning more reflected signals reach the receiver via the antenna, causing complex effects on the direct signal. Therefore, the ΔMP at the DYLL station varies more drastically compared to DYLS. However, specular reflection signals are stronger than diffuse reflection signals, so sea surface reflections have a more severe impact on the direct signal.

[0097] 2.2 Signal Multipath Resistance Analysis Based on Signal-to-Noise Ratio:

[0098] C / N0 can indirectly reflect the degree to which GNSS signals are affected by multipath errors. Based on the method described in Section 2.2, a low-order polynomial fitting is performed on the C / N0 data, and the trend term related to the elevation angle is removed. The remaining fluctuation term can reflect the changing characteristics of the signal's multipath propagation. The differences in the characteristics of the C / N0 fluctuation term of different signals can reflect the degree of influence of multipath propagation on different signals. The experimental results in this part can prove the differences in the multipath resistance performance of signals from another perspective and verify the correctness of the relevant conclusions in Section 2.1. After removing the trend term from the C / N0 data of different signals from different systems, the standard deviation of the remaining fluctuation term is calculated, such as... Figure 5As shown, the C / N0 fluctuation of the same signal from different systems at the DYLL station is smaller than that at the DYLS station because the reflected signal strength at sea is greater, which has a greater impact on the direct signal. The difference in C / N0 fluctuation between different signals of the same system is smaller at the DYLL station, but larger at the DYLS station. This indicates that in a strong multipath environment, the multipath effect has significantly different impacts on different signals, meaning that the multipath resistance of different signals varies. The greater the C / N0 fluctuation, the more severe the multipath influence. The C / N0 fluctuation of the GPS L5 signal, the Galileo E5a signal, and the BDS2 B2I signal is the largest among other signals in this system. This result is consistent with the conclusion in Section 2.1, that is, the multipath resistance of these signals is relatively poor within their respective systems. For BDS3, in the analysis in Section 2.1, the B1C signal exhibits poor multipath resistance, but... Figure 5 The C / N0 signal of the B3I signal exhibits the greatest volatility, leading to inconsistencies between the two methods. We believe this inconsistency may be due to the different modulation scheme of the B1C signal compared to other signals. The B1C signal of BDS3 uses BOC modulation, while other signals use BPSK modulation. When the satellite elevation angle is greater than 5°, the minimum power reaching the receiver antenna output of the B1I, B2I, and B31 signals from the BDS satellite can reach -163 dBW, but the minimum received power of the B1C signal from the MEO satellite is -159 dBW, and that of the IGSO satellite is -161 dBW. Therefore, the lower minimum power reaching the receiver antenna output may also contribute to the inconsistency between the two methods. Since the signal-to-noise ratio (SNR) is a characterization of signal quality, not a direct representation of data quality, the method in Section 2.1 directly evaluates the signal's resistance to multipath propagation based on the quality of the observed data. Therefore, for BDS3, although the two methods differ, we still adhere to the conclusion in Section 2.1, namely, that the B1C signal has poor resistance to multipath propagation.

[0099] Figure 6 The diagram illustrates the C / N0 ratios of different signals in various systems, using G27, E01, C12, and C44 as examples. Notably, the C / N0 ratios of different signals within the same system all exhibit the same magnitude relationship. Figure 6 In addition to what can be observed Figure 5In addition to the previously mentioned characteristic that the C / N0 fluctuation of the DYLS station is greater than that of the DYLL station, it can also be observed that the C / N0 of almost all signals is lower at the DYLS station than at the DYLL station. This is mainly because the multipath effect is more severe at sea, and reflected signals cause more serious interference to direct signals, leading to a decrease in C / N0. However, the C / N0 of the BDS2 B2I signal at the DYLS station is greater than that at the DYLL station. This may be because the reflected signal is at the same frequency as or correlated with the direct signal, resulting in an increase in signal power at the DYLS station.

[0100] Combination Figure 5 , 6 It can be observed that at the DYLS station, the C / N0 of the GPS system's L5 signal is greater than that of the L1 and L2 signals. Similarly, the amplitude of its C / N0 fluctuation term is also greater than that of the L1 and L2 signals. The C / N0 of the Galileo system's E5a signal is between that of the E1 and E5b signals, but the amplitude of its C / N0 fluctuation term is greater than that of the E1 and E5b signals. The C / N0 of the BDS2 B2I signal is greater than that of the B1I and B3I signals, and the amplitude of its C / N0 fluctuation term is also greater than that of the B1I and B3I signals. Based on the magnitude of the C / N0 and the amplitude characteristics of the C / N0 fluctuation term for these different signals, it can be found that due to the different multipath resistance of different signals, a high C / N0 value does not necessarily mean that the signal is less susceptible to interference, nor can it indirectly indicate that the observed value is less affected by multipath effects. This is because the magnitude of the signal's C / N0 is affected not only by interference such as multipath effects, but also by the power output of the satellite signal transmitter and the gain of the receiver antenna.

[0101] 2.3 Stochastic model optimization based on signal resistance to multipath performance differences in strong multipath environments:

[0102] In PPP solution processing, the stochastic model involves the accuracy level of the observations themselves, the dynamic changes of the system, and the stochastic characteristics of the parameters. An appropriate stochastic model can set reasonable weights for carrier phase and pseudorange observations, which is crucial for improving parameter estimation accuracy. Commonly used stochastic models include elevation angle stochastic models and signal-to-noise ratio stochastic models. Low-elevation-angle satellites are more affected by multipath effects and atmospheric delay. The elevation angle stochastic model can set different initial observation noise for different satellites based on their elevation angle, and the weight of the corresponding observation in the solution model can be determined by the magnitude of the observation noise. Setting smaller weights for low-quality observations can reduce their impact on the positioning results. A commonly used sinusoidal function elevation angle stochastic model is shown in Equation 15.

[0103]

[0104] Where m and n are constants, both equal to 1. θ eFor the satellite elevation angle, σ(θ) e Let θ be the standard deviation of the observed noise. The elevation angle can be determined as θ according to Equation 15. e The satellite observation weights, σ(θ) e The larger σ(θ) is, the lower its weight. However, for different signals from the same satellite, or even satellites from different systems at the same elevation angle, σ(θ) has a lower weight. e The same applies. As shown in sections 2.1 and 2.2, the anti-multipath performance of different signals from the same satellite varies, and signals with poor anti-multipath performance from different systems also exhibit different behaviors in strong multipath environments. When performing GNSS positioning calculations in strong multipath environments, it is necessary to assign lower weights to satellites with poor anti-multipath performance. Therefore, we modify Equation 13 into the form shown in Equation 16.

[0105]

[0106] The error amplification factor representing the poor multipath resistance of the S-system. The standard deviation of phase multipath σ(Δm) i This can reflect the stability of the signal's phase multipath. According to... Figure 4 As a result, we calculate MAX ELE σ(Δm) of satellites with poor multipath resistance over angles >60° i The average value of the four signals with poor multipath resistance is used to represent the multipath resistance performance of the signal. Then, Equation 17 is used to calculate the multipath resistance performance of the four signals with poor multipath resistance. The proportional relationship between them. According to Equation 17, P = 2.23:1.16:1.26:1. Since P is only... To examine the proportional relationship, it is necessary to scale up P proportionally to test different orders of magnitude. The magnitude of the impact on the positioning results. As shown in Equation 18, K represents the error factor amplification factor. The larger the value of K, the lower the weight of the four signals L5, E5a, B2I, and B1C relative to other signals in the PPP solution.

[0107]

[0108] A marine uncombined point positioning (UC-PPP) experiment was conducted using the elevation angle model shown in Equation 16. The relative positioning results of the DYLL and DYLS stations were used as the reference value for the UC-PPP positioning of the DYLS station. To ensure that the reference results were not affected by signals with poor multipath resistance, the four signals L5, E5a, B2I, and B1C were not used to establish an ionospherically unaffected combination during baseline calculation, and the cutoff elevation angle was set to 10°. In a strong multipath environment, the root mean square errors in the E, N, and U directions obtained from the elevation angle stochastic model before and after optimization are as follows: Figure 7 As shown, it can be observed that regardless of the cutoff elevation angle set in degrees, compared to the original elevation angle stochastic model, adding an error amplification factor... Afterwards, the accuracy in both the E and N directions improved significantly. As the multipath error factors of the four signals were proportionally increased, their weights in the PPP positioning solution model decreased further, and the positioning accuracy in the E and N directions continued to increase gradually, but the rate of increase decreased. However, after adding an error amplification factor to the elevation angle stochastic model, the positioning accuracy in the U direction decreased. Using the same strategy, the positioning accuracy of the DYLL station and the JFNG and WHU2 IGS stations before and after stochastic model optimization was compared. These stations are all land stations in a weak multipath environment. The results show that using the elevation angle stochastic model with an error amplification factor reduces the accuracy in the E, N, and U directions for these three land stations, and the larger the error factor, the worse the positioning accuracy. The accuracy changes in the E and N directions in strong and weak multipath environments indicate that in a strong multipath environment, reducing the weights of signals with poor multipath resistance such as L5, E5a, B2I, and B1C does indeed help improve horizontal positioning accuracy. Up to the elevation angles of 15° and 20°, the positioning accuracy decreased compared to lower elevation angles, but the decrease in the U-direction was greater than that in the E and N directions, indicating that the reduction in data volume had a greater impact on vertical accuracy than horizontal accuracy. The optimized stochastic model directly reduced the weights of observations at certain frequencies. We believe this operation may have an effect on the final positioning result equivalent to reducing the amount of high-precision observation data, resulting in a larger decrease in vertical accuracy. This negates the accuracy improvement effect brought by multipath propagation, causing the accuracy in the U-direction to decrease instead. Regardless of whether error amplification factors are set for the L5, E5a, B2I, and B1C signals in the elevation angle stochastic model... When the elevation angles are 0°, 5°, and 10°, the positioning accuracy in the E, N, and U directions is less than 15° and 20°, respectively, indicating that the elevation angle stochastic model can effectively suppress multipath errors of low elevation angle signals. However, after setting error factors for these four signals, the horizontal accuracy will be further improved. The positioning error analysis also conversely confirms the conclusions in sections 2.1 and 2.2 regarding the multipath resistance performance of different signals in various positioning systems. The same experiment was also conducted using another set of zero-baseline data from the DYLS station, and its error performance analysis results are consistent with... Figure 7 The result was the same.

[0109] in conclusion:

[0110] This study demonstrates the differences in multipath resistance performance of different signals in GNSS systems using two methods and optimizes the stochastic model based on the conclusions, improving its adaptability in GNSS positioning solution models under strong multipath environments. Previous studies attempted to reflect the multipath resistance performance of different signals using the solution residuals of static stations, but did not yield a complete conclusion. Furthermore, we believe that although theoretically the solution residuals mainly consist of multipath errors, other errors that are not completely and correctly separated, as well as errors introduced by model corrections, are inevitably absorbed into the observation residuals during the solution process, preventing the observation residuals from fully and accurately reflecting the multipath resistance performance of the signal.

[0111] This study reflects the stability of multipath combinations based on inter-epoch single-difference results. This combination is directly based on the original code and phase observations, without introducing additional model errors. Experiments show that code multipath combinations utilize different auxiliary frequencies f. j and f k Extracted and The differences are significant between ocean (strong multipath environment) and land (weak multipath environment) observations. In a weak multipath environment... and There is almost no difference between them, but in a strong multipath environment, the difference is significant. After error isolation and analysis, it was determined that the difference in a strong multipath environment is mainly caused by the epochal variation Δm of phase multipath. Through in-depth comparison and reasoning, it was further determined that the stability of Δm of GPS L5 signal is worse than that of L1 and L2 signals, the stability of Δm of Galileo E5a signal is worse than that of E1 and E5b signals, the stability of Δm of BDS2 B2I signal is worse than that of B1I and B3I signals, and the stability of Δm of BDS3 B1C signal is worse than that of B1I and B3I signals, that is, their anti-multipath performance is poor.

[0112] C / N0 can reflect the degree of influence of multipath reflected signals on direct signals. A low-order fit is performed on the original C / N0 observation data, and then the trend term related to elevation angle is removed, extracting the fluctuation term affected by multipath. This can indirectly reflect the characteristics of multipath variation. This method mainly aims to demonstrate the differences in the multipath resistance performance of GNSS signals from another perspective. For the same signal, the C / N0 fluctuation is smaller on land than at sea, mainly because the signal intensity reflected from the sea surface is greater than that on land, causing a more severe impact on the direct signal. On land, the difference in C / N0 fluctuation amplitude between different signals of the same system is relatively small, but at sea, the difference in C / N0 fluctuation amplitude between different signals of the same system becomes larger, indicating that there are significant differences in the degree of multipath effect on different signals in a strong multipath environment, i.e., different multipath resistance performance. Comparison shows that in a strong multipath environment, the amplitude of the C / N0 fluctuation term of the L5, E5a, and B2I signals is the largest within their respective systems, indicating that they are more affected by multipath than the other two signals in the same system, i.e., their multipath resistance performance is poor, which is consistent with the conclusion obtained by the previous method. However, for BDS3, the conclusion of this method indicates that the B3I signal has the largest fluctuation amplitude, meaning its multipath resistance is poor. This conclusion differs from the conclusion obtained by the first method that the B1C signal of BDS3 has poor multipath resistance compared to the B1I and B3I signals. We believe this may be due to the different modulation scheme of the B1C signal compared to other signals in the BDS system, or the lower minimum power at the receiver output. Since the first method draws conclusions directly from observation data, while C / N0 can only indirectly reflect the characteristics of multipath variation, we still primarily rely on the conclusion obtained by the first method, namely, that the B1C signal has poor multipath resistance compared to the B1I and B3I signals. Based on the magnitude of C / N0 and the amplitude characteristics of the C / N0 fluctuation term for different signals within each system, it can be found that in a strong multipath environment, due to the different multipath resistance performance of different signals, a high C / N0 value does not necessarily mean that the signal is less affected by interference, nor can it indirectly indicate that the observed value is less affected by multipath effects. The C / N0 of a signal is affected not only by interference such as multipath effects, but also by the power output of the satellite signal transmitter and the gain of the receiver antenna.

[0113] Error analysis yielded the standard deviations of Δm for the L5, E5a, B2I, and B1C signals, which characterize phase multipath stability. Based on the ratios of their standard deviations, the multipath resistance performance ratios of the four signals were determined. This ratio was then proportionally amplified as an error amplification factor for these four signals in the elevation angle stochastic model. The addition of the error amplification factor reduced the weight of these signals' observation data in the UC-PPP solution, suppressing their influence on the positioning solution in strong multipath environments. Compared to the original stochastic model, the optimized stochastic model improved horizontal positioning accuracy in strong multipath environments. However, in weak multipath environments, it actually decreased both horizontal and vertical accuracy. This indicates that the optimized stochastic model is indeed effective in strong multipath environments. The positioning accuracy analysis of the stochastic models before and after optimization also strongly supports the conclusions drawn from both methods regarding signal multipath resistance performance evaluation. The conclusions regarding the differences in multipath resistance performance of different system signals provide guidance for GNSS positioning in strong multipath environments. The optimized stochastic model can improve horizontal accuracy, which is of great significance for tasks with high requirements for planar accuracy in strong multipath environments, such as marine navigation and positioning and marine surveying.

[0114] This invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. To provide the public with a thorough understanding of this invention, specific details are described in detail in the following preferred embodiments; however, those skilled in the art will fully understand the invention even without these details. Furthermore, to avoid unnecessary misunderstanding of the essence of this invention, well-known methods, processes, procedures, components, and circuits are not described in detail.

[0115] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A stochastic model optimization method based on the multipath performance differences of GNSS signals, characterized in that, Includes the following steps: S1. Observational data acquisition and environmental classification: In marine and terrestrial environments, stations using the same type of receiver and antenna are deployed to collect GNSS observation data, including GPS L1, L2, L5 signals, Galileo E1, E5a, E5b signals, BDS2 B1I, B2I, B3I signals, and BDS3 B1C, B3I signals. The marine environment is regarded as a strong multipath environment and the terrestrial environment is regarded as a weak multipath environment, so as to establish a comparative observation dataset under different multipath influence scenarios. S2, Multipath Error Inter-Epoch Variation Feature Extraction: In the observation data segment where cycle slip does not occur, a multipath combination is constructed based on the original code and phase observation values. The multipath error variation of different frequency signals is extracted by the inter-epoch single difference method. The stability differences of each frequency signal in strong and weak multipath environments are compared by using different auxiliary frequency combination methods. In this way, the frequency points that exhibit error fluctuations in strong multipath environments are identified, and it is judged that their anti-multipath performance is poor. S3, Error Factor Determination and Proportion Construction: Based on the code multipath combination fluctuation characteristics extracted in a strong multipath environment, the phase multipath error fluctuation intensity related to the frequency signal is deduced, and the relative error intensity ratio is established using GPS L5, Galileo E5a, BDS2 B2I and BDS3 B1C as representative signals. S4, Construction of Elevation Angle Random Model for Fusing Error Factors: Based on the elevation angle random model, an error amplification factor for signals with poor multipath performance is introduced, and its weight in the positioning solution model is controlled by the amplification factor. This constructs an elevation angle random model for fusing signal frequency points to resist multipath performance differences, which is used to dynamically adjust the observation noise level of different signals in the solution. S5, Positioning accuracy analysis and model validity verification: Using the unoptimized and optimized elevation angle stochastic models respectively, single-point positioning calculations were performed on GNSS observation data under a strong multipath environment. By comparing the root mean square values ​​of positioning errors in the E, N, and U directions, the improvement effect of the optimized model on horizontal accuracy was evaluated.

2. The stochastic model optimization method based on the multipath performance differences of GNSS signals according to claim 1, characterized in that, The multipath error epoch change feature extraction in S2 includes: S21, Observation Model Construction: Based on the composition of GNSS observation data, a code observation model and a carrier observation model are established at frequency i to express the influence paths of various error components in the observation data, represented as: P i =ρ+c(δt r -δt s )+I i +T+M i +d r,i +d s,i +ε(P i ); L i =ρ+c(δt r -δt s )-I i +T+m i +b r,1 +b s,1 +λ i N i +ε(L i ); Where P and L represent code observations and carrier phase observations, respectively, i represents different frequencies, ρ represents the geometric distance from the satellite to the station antenna, c is the speed of light in vacuum, and δt is the velocity of light. r and δt s I represents the clock difference between the receiver clock and the satellite clock, respectively. i Indicates ionospheric delay, T is tropospheric delay, and M is tropospheric delay. i and m i These represent code multipath and carrier phase multipath, respectively, d r,i and d s,i These represent the frequency-dependent code hardware delays at the receiver and satellite ends, respectively, b r,i and b s,i λ represents the frequency-dependent phase hardware delay at the receiver and satellite ends, respectively. i Represents frequency f i The corresponding wavelength, N i For carrier phase integer ambiguity, ε(P) i ) and ε(L i These represent the observation noise for the code and carrier phase, respectively. S22, Code multipath combination construction: Construct the code multipath combination term between the main frequency i and the auxiliary frequency j, and then extract the frequency-related observation error term, represented as: Among them, MP i,j These are code multipath observations at frequency i; S23, Multi-frequency combination term expansion analysis: The combination terms are algebraically expanded to reveal the weights and propagation paths of each error component, distinguishing between phase multipath error, observation noise term, and ambiguity term, expressed as: S24, Multi-path combination mean removal: Within a cycle-slip-free arc segment, extract and remove the average value of the combination terms to obtain the true trend of the combination's change within that arc segment, expressed as: S25, Extraction of inter-epoch change trends: Perform epoch differencing on the combined terms after removing the average value, extract its gradient over continuous time, and construct an error change sequence, represented as:

3. The stochastic model optimization method based on the multipath performance differences of GNSS signals according to claim 2, characterized in that, The error term of the inter-epoch change in S25 is expanded as follows:

4. The stochastic model optimization method based on the multipath performance differences of GNSS signals according to claim 3, characterized in that, The determination of error factors and the construction of proportions in S3 include: S31, Multipath Combination Standard Deviation Extraction: Extraction of code multipath combination terms for each frequency signal. Perform epoch differencing and calculate its standard deviation over the cycle-slip-free arc segment, denoted as . S32, Phase multipath error standard deviation inverse calculation: Based on the multipath propagation model and frequency combination coefficients, Convert to phase multipath error standard deviation Represented as: in, It is the abnormal fluctuation of ΔMP ij standard deviation Yes, Δm j standard deviation It is Δm j The corresponding coefficient.

5. The stochastic model optimization method based on the multipath performance differences of GNSS signals according to claim 4, characterized in that, The elevation angle stochastic model for the fusion error factor in S4 includes: S41, Elevation Angle Model Construction: A sinusoidal function stochastic elevation angle model is established based on the satellite elevation angle to describe the variation trend of observation noise with elevation angle, expressed as: Where m and n are constants, θ e For the satellite elevation angle, σ(θ) e ) represents the standard deviation of the observed noise; S42, Introducing a frequency point error factor for weighted correction: Based on the constructed sinusoidal function elevation angle stochastic model, a frequency point differential error factor is introduced. Construct a frequency-dependent random error model, expressed as:

6. The stochastic model optimization method based on the multipath performance differences of GNSS signals according to claim 5, characterized in that, The frequency point difference error factor By using the phase multipath error standard deviation σ(Δm) i The result is calculated using the set magnification factor K, and expressed as: EF i =σ(Δm i )·K.

7. The stochastic model optimization method based on the multipath performance differences of GNSS signals according to claim 6, characterized in that, The positioning accuracy analysis and model validity verification in S5 include: S51, Model Replacement and Solution Comparison: Based on DYLS station data, non-difference, non-combination PPP solution processing was performed using the sinusoidal function elevation angle stochastic model before and after correction. S52, RMS Error Assessment: Set multiple elevation angle thresholds, statistically analyze the positioning RMS errors in the E, N, and U directions, and verify the improvement effect of the optimized model on planar positioning accuracy in a strong multipath environment.

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