A RTK integrity monitoring method considering integer ambiguity failure modes

Abstract

The present invention relates to an RTK integrity monitoring method taking into account integer ambiguity failure modes, comprising: calculating the probability of integer ambiguity fixation success and the probability of integer ambiguity fixation failure; comparing a preset integrity risk index with the obtained probability of integer ambiguity fixation failure, and simplifying the number of integer ambiguity fixation failure modes; evenly distributing the preset integrity risk index to the integer ambiguity fixation success mode and the integer ambiguity fixation failure mode after the number is simplified, and calculating the vertical protection level using the evenly distributed integrity risk index; comparing the obtained vertical protection level with the preset vertical alarm limit, if the vertical protection level is less than the vertical alarm limit, it means that the current system meets the integrity requirement; if the vertical protection level is greater than or equal to the vertical alarm limit, it means that the current system does not meet the integrity requirement.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite navigation, and particularly relates to an RTK integrity monitoring method considering the failure mode of integer ambiguity. Background Art

[0002] The Global Navigation Satellite System (GNSS) has powerful functions such as navigation, positioning, and timing. It is an important means to help realize the informatization and modernization of transportation, covering multiple typical application scenarios such as sea, land, and air, and is widely used in fields such as transportation, military, and agriculture. For example, fully automatic aircraft landing, fully automatic carrier-based aircraft landing, vehicle-mounted navigation systems, driverless, intelligent traffic control, intelligent marine operations, intelligent agricultural machinery collaborative operations, and so on.

[0003] The application fields of GNSS are closely related to the safety of users' lives and property. Therefore, the transformation of GNSS positioning services from high precision to high reliability is an inevitable trend. The reliability of navigation services is measured by the performance index of integrity. RTK (Real-time kinematic) refers to real-time kinematic differential positioning technology, also known as carrier phase differential positioning technology. It is a kind of GNSS relative positioning technology, which is a differential method for real-time processing of carrier phase observations at two measurement stations. The carrier phase collected by the reference station is sent to the user receiver for differential calculation of coordinates, and centimeter-level positioning accuracy can be provided. For RTK positioning technology, carrier phase integrity monitoring is a key means to ensure and measure the reliability of navigation services, especially for the application scenario of fully automatic carrier-based aircraft landing.

[0004] By using the double-difference carrier phase observation model, high-precision positioning results can be obtained. However, since the phase observation can only measure the phase less than one week, the initial integer cycle number and the accumulated integer cycle number cannot be measured, that is, there is an integer ambiguity. The ambiguity of whole cycles, also known as the unknown integer number of cycles, is the unknown integer number of cycles corresponding to the first observation value of the phase difference between the carrier phase and the reference phase in the carrier phase measurement of the global positioning system technology. Correctly determining the ambiguity of whole cycles is one of the very important and must-be-solved problems in carrier phase measurement. However, it is difficult for the existing technology to fix the ambiguity of whole cycles with 100% accuracy. The fixed failure of the ambiguity of whole cycles will lead to a positioning deviation of decimeter level or even larger. In addition, the number of events of fixed failure of the ambiguity of whole cycles is infinite, and it is unrealistic to calculate an infinite sequence during integrity monitoring. Therefore, it is difficult to avoid the problems brought by the fixed failure of the ambiguity of whole cycles during carrier phase integrity monitoring. Summary of the Invention

[0005] Since the carrier phase integrity monitoring is limited by the fixing of the integer ambiguity, how to accurately summarize the impact of the failure of integer ambiguity fixing is the key to truly improving the positioning reliability.

[0006] To solve the above problems, the present invention designs an RTK integrity monitoring method considering the failure mode of integer ambiguity, which includes:

[0007] Step S1) Calculate the probability of successful integer ambiguity fixing and the probability of failed integer ambiguity fixing according to the statistical characteristics of the floating-point solution of the integer ambiguity;

[0008] Step S2) Compare the preset integrity risk index with the obtained probability of failed integer ambiguity fixing, and exclude the failure modes of integer ambiguity fixing whose probability of failed integer ambiguity fixing is less than or equal to the product of the preset integrity risk index and the screening factor, so as to reduce the number of failure modes of integer ambiguity fixing to a finite number;

[0009] Step S3) Evenly distribute the preset integrity risk index to the successful integer ambiguity fixing mode and the failure modes of integer ambiguity fixing reduced to a finite number, and obtain the integrity risk index assigned to each integer ambiguity fixing mode;

[0010] Step S4) Calculate the vertical protection level by using the evenly distributed integrity risk index obtained;

[0011] Step S5) Compare the obtained vertical protection level with the preset vertical warning limit. If the vertical protection level is less than the vertical warning limit, it means that the current system meets the integrity requirements; if the vertical protection level is greater than or equal to the vertical warning limit, it means that the current system does not meet the integrity requirements.

[0012] The beneficial effects of the present invention are as follows:

[0013] The present invention designs an RTK integrity monitoring method considering the integer ambiguity failure mode. Aiming at the problem that it is difficult to effectively monitor the carrier phase integrity due to countless integer ambiguity fixing failure events, the present invention calculates the probability of successful integer ambiguity fixing and the probability of integer ambiguity fixing failure according to the statistical characteristics of the integer ambiguity float solution, simplifies the infinite sorting of integer ambiguity fixing failure events into a finite number, evenly distributes the integrity risk index for the successful integer ambiguity fixing mode and the fixing failure mode, constructs the vertical protection level considering the successful and failed integer ambiguity fixing modes, and compares it with the preset vertical warning limit to achieve the purpose of effectively monitoring the carrier phase integrity. The RTK integrity monitoring method provided by the present invention effectively completes the monitoring of the carrier phase integrity considering the integer ambiguity fixing failure mode for RTK positioning technology, provides the most important credible basis for users in application scenarios such as sea, land, and air when using navigation services, ensures the reliability of navigation services, and is of great significance for ensuring high-precision and high-reliability navigation services in sea, land, and air application scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 FIG. is a flowchart of an RTK integrity monitoring method considering the integer ambiguity failure mode provided by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0015] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0016] Reference Figure 1 , the present invention proposes an RTK (Real - Time Kinematic) integrity monitoring method considering the integer ambiguity failure mode, and the method includes:

[0017] Step S1) Calculate the probability of successful integer ambiguity fixing and the probability of integer ambiguity fixing failure according to the statistical characteristics of the integer ambiguity float solution.

[0018] Obtain the float solution of the position x and the integer ambiguity z and its variance - covariance matrix through existing known methods, where the float solution of the integer ambiguity The statistical characteristics of generally can be considered to follow a normal distribution z represents the true value of the integer ambiguity, represents the variance of the integer ambiguity. Therefore, the probability of successful integer ambiguity fixing (i.e., correct integer ambiguity solution) can be expressed as:

[0019]

[0020] In Equation (1), PCF represents the probability of successful integer ambiguity resolution, N represents the number of currently visible satellites, t represents the integration variable, exp represents the natural exponential function, i.e., exp(*) = e^*, det(*) represents the determinant of matrix *, and S 0 represents the rounding domain corresponding to successful integer ambiguity resolution. It should be noted that the rounding domains of different integer ambiguity resolution algorithms are generally different.

[0021] Similarly, the probability of failure in the i-th week of integer ambiguity resolution (i.e., the failure of integer ambiguity solution) can be obtained as:

[0022]

[0023] In Equation (2), PIF i represents the probability of failure in the i-th week of integer ambiguity resolution. The physical meaning of the failure in the i-th week of integer ambiguity resolution refers to the number of cycles by which the integer ambiguity solution value differs from the true value of the integer ambiguity. S i represents the rounding domain corresponding to the failure in the i-th week of integer ambiguity resolution. The meanings of other parameters are the same as those in Equation (1).

[0024] Step S2) Compare the preset integrity risk index IR req with the obtained probability of failure in integer ambiguity resolution, and exclude the failure modes of integer ambiguity resolution whose probability of failure in integer ambiguity resolution is less than or equal to the product of the preset integrity risk index IR req and the screening factor ef, so as to reduce the infinite number of failure modes of integer ambiguity resolution to a finite number.

[0025] According to the probability formulas of successful and failed integer ambiguity resolution obtained in Step S1, the probability of successful integer ambiguity resolution and the probability of failed integer ambiguity resolution can be obtained. Considering that the number of events of failed integer ambiguity resolution (which can also be called the failure modes of integer ambiguity resolution) is infinite, it is not practical to calculate an infinite sequence, and the infinite number of events of failed integer ambiguity resolution needs to be reduced to a finite number.

[0026] Therefore, the present invention selects all the failure events of integer ambiguity resolution whose probability of failure is greater than the product of the preset integrity risk index IR req and the screening factor ef as the failure modes of integer ambiguity resolution that need to be considered; the remaining failure modes of integer ambiguity resolution can be directly considered to definitely cause the vertical positioning error to exceed the threshold value and be excluded, that is, the probability of failure in integer ambiguity resolution is less than or equal to the preset integrity risk index IR reqExclude the integer ambiguity fixing failure modes that are the product of the screening factor ef, obtaining a finite number of integer ambiguity fixing failure modes. The finite set of simplified integer ambiguity fixing failure modes is:

[0027] Ω req ={Ω i |PIF i >ef×IR req , i ∈ Z, i ≠ 0} (3)

[0028] In Equation (3), Ω req represents the finite set of simplified integer ambiguity fixing failure modes, Ω i represents the simplified integer ambiguity fixing failure mode for i weeks, PIF i represents the probability of integer ambiguity fixing failure for i weeks, IR req represents the preset integrity risk index, which is determined by the required navigation performance of the system and is generally set to 10 -7 , ef represents the screening factor, which is an empirical value. In this invention, the empirical value 0.001 is selected, and Z represents all integers.

[0029] Since as the number of weeks of integer ambiguity fixing failure increases, the corresponding probability of fixing failure decreases significantly until the probability of integer ambiguity fixing failure is less than or equal to the product of the preset integrity risk index IR req and the screening factor ef, ef×IR req . Select the integer ambiguity fixing failure events whose probabilities of all integer ambiguity fixing failures are greater than the product of the preset integrity risk index IR req and the screening factor ef as the integer ambiguity fixing failure modes to be considered. Then, i in the finite set of integer ambiguity fixing failure modes has a maximum value. Take the maximum value of i in the finite set of integer ambiguity fixing failure modes as the maximum number of failure weeks I max of the integer ambiguity.

[0030] Through the above simplification process for the infinite number of integer ambiguity fixing failure modes, the infinite number of integer ambiguity fixing failure events becomes a finite number, solving the problem that an infinite sequence cannot be calculated.

[0031] Step S3) Evenly distribute the preset integrity risk index IR req to the integer ambiguity fixing success modes and the simplified finite number of integer ambiguity fixing failure modes, obtaining the integrity risk index assigned to each integer ambiguity fixing mode.

[0032] Assume that only one satellite has integer ambiguity fixing failure. According to the total probability formula, the overall integrity risk closed calculation formula of the navigation system can be listed as:

[0033]

[0034] In Equation (4), IR req represents a preset integrity risk index, N represents the number of currently visible satellites, PCF represents the probability of successful integer ambiguity fixing, and PIF i,j represents the probability that the integer ambiguity of the j-th satellite fails to be fixed for i weeks, and IR CF represents the integrity risk caused by successful integer ambiguity fixing, and IR IFi,j represents the integrity risk caused by the integer ambiguity of the j-th satellite failing to be fixed for i weeks. The coefficient 2 in Equation (4) is used to distinguish positive and negative integer ambiguity deviations.

[0035] Based on the maximum number of failed weeks of integer ambiguity I determined according to Equation (3) max , Equation (4) is rearranged as follows:

[0036]

[0037] According to the principle of equal distribution, the preset integrity risk index IR req is evenly distributed to the successful integer ambiguity fixing mode and simplified to a finite number of integer ambiguity fixing failure modes. Furthermore, the integrity risk index IR evenly distributed to the successful integer ambiguity fixing mode and a finite number of fixing failure modes can be obtained H as:

[0038]

[0039] In Equation (6), IR H represents the integrity risk index evenly distributed to the successful integer ambiguity fixing mode and simplified to a finite number of fixing failure modes, and IR req represents the preset integrity risk index, N represents the number of currently visible satellites, PCF represents the probability of successful integer ambiguity fixing, and PIF i,j represents the probability that the integer ambiguity of the j-th satellite fails to be fixed for i weeks, and I max represents the maximum number of failed weeks of integer ambiguity. The coefficient 2 is used to distinguish positive and negative integer ambiguity deviations.

[0040] The integrity risk index is allocated to the simplified finite number of integer ambiguity fixing failure modes, providing the integrity risk index for subsequent calculation of the vertical protection level.

[0041] Step S4) uses the integrity risk index IR evenly distributed to the successful integer ambiguity fixing mode and a finite number of fixing failure modes obtained in step S3 H to calculate the vertical protection level.

[0042] After the integer ambiguity is fixed (including successful and failed fixings), the position float solution is corrected, and the mean and variance of the position corrected solution are as follows:

[0043]

[0044] In Equation (7), E(*) represents the mean operation, and D(*) represents the variance operation. represents the position corrected solution under the condition that the integer ambiguity fixing of the j-th satellite fails for i weeks. i = 0 indicates that the integer ambiguity is successfully fixed, z represents the true value of the integer ambiguity, represents the position float solution, represents the float solution of the integer ambiguity, is the variance-covariance matrix of the position float solution is the variance-covariance matrix of the float solution of the integer ambiguity is the float solution of the integer ambiguity is the variance-covariance matrix of

[0045] represents and the covariance matrix of, representing the correlation between and , and f j represents the (N - 1)-dimensional column vector determined by the faulty satellite j, containing elements 0 and 1. Element 0 indicates that the integer ambiguity is successfully fixed, and element 1 indicates that the integer ambiguity fixing fails. N represents the number of currently visible satellites.

[0046] Therefore, for the case where the integer ambiguity is successfully fixed and when the integer ambiguity of the j-th satellite fails for i weeks, the method for obtaining the vertical protection level is as follows:

[0047]

[0048] In Equation (8), VPL 0 represents the vertical protection level when the integer ambiguity is successfully fixed, and VPL i,j represents the vertical protection level when the integer ambiguity of the j-th satellite fails for i weeks. erf -1 (*) represents the inverse function of the error function, represents the position corrected solution when the integer ambiguity is successfully fixed, represents the position corrected solution when the integer ambiguity of the j-th satellite fails for i weeks, where i is not 0. IR H represents the integrity risk index evenly distributed for the successful integer ambiguity fixing mode and a reduced number of fixed failure modes. E(*) represents the mean operation, and D(*) represents the variance operation.

[0049] Taking the vertical protection level as the upper boundary of the positioning error, it should envelope the positioning error in both the successful and failed integer ambiguity resolution modes. Therefore, the finally obtained vertical protection level is:

[0050] VPL = max(VPL 0 VPL i,j ), i = 1:I max , j = 1:N - 1 (9)

[0051] In Equation (9), VPL represents the vertical protection level, VPL 0 represents the vertical protection level when the integer ambiguity resolution is successful, and VPL i,j represents the vertical protection level when the integer ambiguity of the j-th satellite fails to resolve for i weeks. i represents the number of weeks when the integer ambiguity resolution fails for i weeks, j represents the j-th satellite when the integer ambiguity resolution fails for i weeks, I max represents the maximum number of weeks of integer ambiguity resolution failure, and N represents the number of currently visible satellites.

[0052] The vertical protection level considering both the successful and failed integer ambiguity resolution modes is constructed and used as the test statistic for carrier phase integrity monitoring, which can be used as the basis for integrity monitoring.

[0053] Step S5) Compare the vertical protection level obtained in step S4 with the preset vertical alarm limit to determine whether the current system meets the integrity requirements: If the vertical protection level is less than the vertical alarm limit, it means the current system meets the integrity requirements; if the vertical protection level is greater than or equal to the vertical alarm limit, it means the current system does not meet the integrity requirements.

[0054] Taking the preset vertical alarm limit VAL as the test threshold, compare the final vertical protection level VPL obtained according to step S4 with the vertical alarm limit VAL to determine whether the current system meets the integrity requirements: If the vertical protection level VPL < vertical alarm limit VAL, it indicates that the current system meets the integrity requirements and the current system is available; if the vertical protection level VPL ≥ vertical alarm limit VAL, it indicates that the current system does not meet the integrity requirements and the current system is not available.

[0055] The above content further elaborates on the present invention in combination with specific embodiments. It cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention belongs, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, which should all be regarded as falling within the protection scope determined by the claims submitted for the present invention.

Claims

1. A method for monitoring RTK integrity taking into account integer ambiguity failure modes, comprising: Step S1) calculating the probability of successful integer ambiguity fixation and the probability of failed integer ambiguity fixation according to the statistical characteristics of the integer ambiguity floating point solution; Step S2) comparing a preset integrity risk index with the obtained probability of integer ambiguity fixation failure, excluding integer ambiguity fixation failure modes whose probability of integer ambiguity fixation failure is less than or equal to the product of the preset integrity risk index and the screening factor, thereby simplifying the number of integer ambiguity fixation failure modes to a finite number; Step S3) evenly distribute the preset integrity risk index to the integer ambiguity fixation success mode and the integer ambiguity fixation failure mode simplified to a finite number, to obtain the integrity risk index evenly distributed to the integer ambiguity fixation success mode and the finite number of fixation failure modes; Step S4) calculating the vertical protection level using the obtained averagely distributed integrity risk index; Step S5) compares the obtained vertical protection level with the preset vertical alarm limit. If the vertical protection level is less than the vertical alarm limit, it means that the current system meets the integrity requirements; if the vertical protection level is greater than or equal to the vertical alarm limit, it means that the current system does not meet the integrity requirements.

2. The RTK integrity monitoring method taking into account integer ambiguity failure modes according to claim 1, wherein: In step S1, the method for calculating the probability of successful integer ambiguity fix is: The method to calculate the probability of integer ambiguity fix failure is: In equations (1) and (2), PCF represents the probability of successful integer ambiguity fixation, and PIF i represents the probability of integer ambiguity fix failure i weeks, t represents the integral variable, exp represents the natural exponential function, N represents the number of currently visible satellites, det(*) represents the determinant of the matrix *, represents the integer ambiguity variance, S0 represents the corresponding integration domain when the integer ambiguity is successfully fixed; S i It is represented as the integration domain corresponding to the integer ambiguity fixation failure i.

3. The RTK integrity monitoring method taking into account integer ambiguity failure modes according to claim 2, wherein: In step S2, the number of integer ambiguity fixation failure modes is simplified to a finite number of integer ambiguity fixation failure modes: Oh req ={Ω i |PIF i >ef×IR req ,i∈Z,i≠0} (3) In formula (3), Ω req represents the finite set of simplified integer ambiguity fixing failure modes, Ω i Indicates the simplified integer ambiguity fixation failure i-week mode, PIF i represents the probability of integer ambiguity fixation failure for i weeks, IR req represents the preset integrity risk index, ef represents the screening factor, and Z represents all integers; According to formula (3), the maximum value of i in the finite number of integer ambiguity fixed failure modes is obtained as the maximum integer ambiguity failure cycle number I max .

4. The RTK integrity monitoring method taking into account integer ambiguity failure modes according to claim 3, wherein: In step S3, the integrity risk index averagely allocated to the integer ambiguity fixation success mode and a limited number of fixation failure modes is: In formula (6), IR H It is expressed as the integrity risk index averaged over the fixed success mode of the whole fuzzy cycle and a finite number of fixed failure modes, IR req represents the preset integrity risk index, N represents the number of currently visible satellites, PCF represents the probability of successful whole-week ambiguity fixation, PIF i,j represents the probability that the integer ambiguity fix of the jth satellite fails for i weeks, I max Indicates the maximum number of failed integer ambiguity cycles.

5. The RTK integrity monitoring method taking into account integer ambiguity failure modes according to claim 4, wherein: In step S4, the method for calculating the vertical protection level is: VPL=max(VPL0 VPL i,j ),i=1:I max ,j=1:N-1 Among them, VPL represents the vertical protection level, VPL0 represents the vertical protection level when the integer ambiguity is successfully fixed, and VPL i,j represents the vertical protection level when the integer ambiguity fixation of the j-th satellite fails for i weeks, i represents the integer ambiguity fixation failure for i weeks, j represents the j-th satellite with the integer ambiguity fixation failure for i weeks, I max represents the maximum number of failed integer ambiguity cycles, and N represents the number of currently visible satellites; The method for calculating the vertical protection level VPL0 when the integer ambiguity is successfully fixed is: Where: D(*) represents the variance operation, It represents the position correction solution when the integer ambiguity is fixed successfully, erf -1 (*) represents the inverse function of the error function, IR H The integrity risk index is expressed as the average distribution of the fixed success mode of the whole ambiguity and a finite number of fixed failure modes; Calculate the vertical protection level VPL when the integer ambiguity fixation of the j-th satellite fails for i weeks i,j The method is: Among them: E(*) represents mean operation, D(*) represents variance operation, It represents the position correction solution of the jth satellite when the integer ambiguity fix fails for i weeks, where i is not 0, erf -1 (*) represents the inverse function of the error function, IR H It is expressed as the integrity risk indicator averaged over the fixed success mode of the integer ambiguity and a finite number of fixed failure modes.

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