A multi-receiver differential satellite set selection method for carrier phase cooperative differentiation

Abstract

The present invention relates to a multi-receiver differential satellite set selection method for carrier phase cooperative differential, comprising: performing real-time differential positioning of carrier phase according to differential observations of multiple reference receivers and original observations of a single reference receiver, and generating all differential satellite subsets based on a multiple hypothesis solution separation method; calculating the probability of successful integer ambiguity resolution and the probability of failed integer ambiguity resolution of each differential satellite subset according to the statistical characteristics of integer ambiguity floating point solutions; simplifying the number of integer ambiguity resolution failure events to a finite number; calculating the integrity risks of all differential satellite subsets; and selecting the differential satellite subset with the lowest integrity risk based on a minimum integrity risk criterion.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite navigation, and particularly relates to a method for selecting a multi-receiver differential satellite set for carrier phase collaborative differential. Background Art

[0002] The Global Navigation Satellite System (GNSS) has powerful functions such as navigation, positioning, and timing, and can provide all-round, all-weather, and all-time navigation and positioning services, which can be widely applied to various civil and military carriers on land, at sea, and in the air. For the navigation application of an aircraft in the final approach stage of flight, the relative position is usually obtained by using Real Time Kinematic (RTK) of carrier phase. However, its positioning accuracy and integrity are affected by relevant risk sources such as the satellite side, the atmosphere side, and the receiver side. To address the above risk sources, a multi-reference receiver collaborative method is usually adopted for integrity monitoring.

[0003] However, the multi-reference receiver cannot monitor the relevant risk sources at the user side. For example, the integer ambiguity resolution fails. The resolved failed integer ambiguity will cause a decrease in positioning accuracy and an increase in uncertainty, seriously endangering the integrity of the navigation system. Considering that the integer ambiguity resolution process is closely related to the satellites used for positioning resolution, although the number of satellites generally shows a positive correlation with the positioning accuracy, an increase in the number of satellites may cause an increase in the risk of integer ambiguity resolution failure, thereby leading to a sharp decrease in the system integrity. Therefore, it is necessary to develop a method for reasonably selecting available satellites from the multi-reference receiver differential satellite set, so as to minimize the integrity risk caused by integer ambiguity resolution failure, and thus greatly improve the system integrity. Summary of the Invention

[0004] To solve the above problems, the present invention designs a method for selecting a multi-receiver differential satellite set for carrier phase collaborative differential, including:

[0005] Step S1) Perform real-time carrier phase differential positioning based on the differential observations of multiple reference receivers and the original observations of a single reference receiver, and generate all differential satellite subsets based on the multiple hypothesis solution separation method;

[0006] Step S2) Calculate the probability of successful integer ambiguity resolution and the probability of resolution failure for each differential satellite subset according to the statistical characteristics of the floating-point solution of the integer ambiguity.

[0007] Step S3) Compare the preset integrity risk index with the obtained probability of integer ambiguity resolution failure, exclude the integer ambiguity resolution failure events where the probability of integer ambiguity resolution failure is less than the product of the preset integrity risk index and the loss factor, and simplify the number of integer ambiguity resolution failure events to a finite number.

[0008] Step S4) Use the vertical warning limit as the detection threshold to calculate the integrity risk of all differential satellite subsets.

[0009] Step S5) Select the differential satellite subset with the lowest integrity risk based on the minimum integrity risk criterion.

[0010] The beneficial effects of the present invention are as follows:

[0011] A method for selecting a multi-receiver differential satellite set for carrier-phase cooperative differential provided by the present invention makes full use of multiple reference receivers for loopback monitoring, generates all differential satellite subsets based on the multiple hypothesis solution separation method, quantifies the solution rate of all integer ambiguity resolutions by combining the statistical distribution characteristics of the integer ambiguity floating-point solution, thereby calculating the integrity risk of each differential satellite subset, and selects the best differential satellite subset based on the minimum integrity risk criterion. The selected differential satellite subset has the minimum integrity risk, truly improving the integrity of navigation and positioning, and assisting users to achieve high-precision and high-reliability navigation and positioning. Description of the Drawings

[0012] Figure 1 It is a flowchart of a method for selecting a multi-receiver differential satellite set for carrier-phase cooperative differential provided by the present invention. Detailed Embodiment

[0013] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the 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 the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0014] Next, through embodiments and in conjunction with the attached Figure 1 , the technical solutions of the present invention will be further specifically described.

[0015] The present invention provides a method for selecting a multi-receiver differential satellite set for carrier-phase cooperative differential, including:

[0016] Step S1) Perform carrier-phase real-time differential positioning based on the differential observations of multiple reference receivers and the original observations of a single reference receiver, and generate all differential satellite subsets based on the multiple hypothesis solution separation method.

[0017] Carrier phase real-time differential positioning is performed using differential observations generated based on multiple reference receivers and the original observations of a single reference receiver. Assuming that there are N satellites providing carrier phase real-time differential positioning (hereinafter referred to as: differential satellites), the corresponding complete set of differential satellites can be expressed as:

[0018] χ all ={SV 1 SV 2 … SV i … SV N} (1)

[0019] In Equation (1), χ all represents the complete set of available differential satellites, and SV i represents the index of the available differential satellite i. Considering that carrier phase real-time differential positioning requires at least 4 available satellites, for N available satellites, based on the Multiple Hypothesis Solution Separation method (MHSS), the number of effective differential satellite subsets that can be generated is:

[0020]

[0021] In Equation (2), N sub represents the number of differential satellite subsets, C represents the combination operator, and N represents the number of available satellites.

[0022] All effective differential satellite subsets are generated, which can increase the selectable differential satellite sets.

[0023] Step S2) According to the statistical characteristics of the float solution of the integer ambiguity, calculate the probability of successful integer ambiguity resolution and the probability of failure of resolution for each differential satellite subset.

[0024] For a certain differential satellite subset χ j , where j ∈ [1, N sub , according to the statistical characteristics of the float solution of the integer ambiguity , the method for calculating the probability of successful integer ambiguity resolution is:

[0025]

[0026] In Equation (3), PCF represents the probability of successful integer ambiguity resolution, represents the probability of successful integer ambiguity resolution of the differential satellite subset χ j , П(*) represents the product symbol, n represents the number of integer ambiguities of the differential satellite subset χ j , i represents the satellite index in the differential satellite subset χ j , and Ф(x) represents the cumulative probability density function of the standard normal distribution. Indicates the satellite index number SV obtained using the observations of the differential satellite subset χ j and the variance corresponding to the floating-point solution of the integer ambiguity of the satellite with i Indicates the floating-point solution of the integer ambiguity.

[0027] Similarly, for the integer ambiguity resolution failure event k, the method for calculating the corresponding probability of integer ambiguity resolution failure is as follows:

[0028]

[0029] In Equation (4), PIF represents the probability of integer ambiguity resolution failure, Indicates the probability of integer ambiguity resolution failure corresponding to the integer ambiguity resolution failure event k of the differential satellite subset χ j , k represents the k-th integer ambiguity resolution failure event (i.e., the integer ambiguity resolution failure event k), the number of which is infinite, П(*) represents the product symbol, n represents the number of integer ambiguities of the differential satellite subset χ j , i represents the satellite index in the differential satellite subset χ j , Ф(x) represents the cumulative probability density function of the standard normal distribution, f k Indicates the fault unit vector corresponding to the integer ambiguity resolution failure event k, Δz k Indicates the magnitude of the integer ambiguity deviation corresponding to the integer ambiguity resolution failure event k, Indicates the satellite index number SV obtained using the observations of the differential satellite subset χ j and the variance corresponding to the floating-point solution of the integer ambiguity of the satellite with i

[0030] Using Equations (3) and (4), the probability of successful integer ambiguity resolution and the probability of integer ambiguity resolution failure can be calculated.

[0031] Step S3) Compare the preset integrity risk index IR req with the obtained probability of integer ambiguity resolution failure, and exclude the integer ambiguity resolution failure events whose probability of integer ambiguity resolution failure is less than the product of the preset integrity risk index and the loss factor lf, so as to simplify the number of integer ambiguity resolution failure events to a finite number.

[0032] Considering that the number of integer ambiguity resolution failure events is infinite and it is not practical to calculate an infinite sequence. Therefore, through a large number of experiments, it is determined that the probability of all integer ambiguity resolution failures is less than the preset integrity risk index IR req ​​The event of integer ambiguity resolution failure that is multiplied by the loss factor lf will definitely trigger an integrity risk, that is, the probability of all integer ambiguity resolution failures is less than the product IR of the preset integrity risk index and the loss factor req The probability that the integer ambiguity resolution failure event of ×lf triggers an integrity risk is 100%, and it needs to be excluded, so as to obtain a finite number of integer ambiguity resolution failure events. Therefore, the finite number set of the simplified integer ambiguity resolution failure events is as follows:

[0033]

[0034] In Equation (5), represents the finite number set of integer ambiguity resolution failure events under the simplified differential satellite subset χ j The probability of integer ambiguity resolution failure corresponding to the integer ambiguity resolution failure event k of the differential satellite subset χ represents the differential satellite subset χ j The probability of integer ambiguity resolution failure corresponding to the integer ambiguity resolution failure event k; k represents the kth integer ambiguity resolution failure event (i.e., the integer ambiguity resolution failure event k), the number of which is infinite, and IR req represents the preset integrity risk index, lf represents the loss factor, and Z represents all integers, which represents the number of weeks of integer ambiguity failure

[0035] The preset integrity risk index IR req is determined by the integrity risk required by the system and belongs to a preset value, generally set to 10 -7 . The loss factor lf is an empirical value, and the empirical value 0.001 is selected in the present invention. Therefore, the simplified method adopted in the present invention is not to consider the integer ambiguity resolution failure events whose probability of integer ambiguity resolution failure is lower than the integrity risk index by three orders of magnitude

[0036] According to Equation (5), the present invention selects all integer ambiguity resolution failure events whose probability is greater than or equal to IR req ×lf as the integer ambiguity resolution failure events that need to be considered. In this way, k in the finite number set of integer ambiguity resolution failure events has a specific value. The present invention uses k max to represent the maximum value of k, and uses k max to represent the number of elements in the finite number set of integer ambiguity resolution failure events under the differential satellite subset χ j , that is, k max is the number of integer ambiguity resolution failure events obtained after simplification

[0037] Simplify the infinite number of integer ambiguity resolution failure events, so that the infinite number of integer ambiguity resolution failure events becomes a finite number, solving the problem that an infinite sequence cannot be calculated, and thus the integrity risk of all differential satellite subsets can be calculated.

[0038] Step S4) Use the vertical alert limit VAL as the detection threshold to calculate the integrity risk of all differential satellite subsets.

[0039] Take all possible events CF (resolution success events) and IF i (infinite resolution failure events) involved in the integer ambiguity resolution into account, and based on the calculation methods of the probability of integer ambiguity resolution success and the probability of integer ambiguity resolution failure, construct the calculation method of the integrity risk of the differential satellite subset χ j The calculation method of the integrity risk is as follows:

[0040]

[0041] In Equation (6), represents the integrity risk of the differential satellite subset χ j , P{*} represents the probability of the occurrence of event *, represents the integer ambiguity resolution success event of the differential satellite subset χ j , PCF χj represents the probability of integer ambiguity resolution success of the differential satellite subset χ j , represents the k-th integer ambiguity resolution failure event in the differential satellite subset χ j , represents the probability of integer ambiguity resolution failure corresponding to the integer ambiguity resolution failure event k of the differential satellite subset χ j , represents the position fixed solution corrected by the integer ambiguity, represents the position fixed solution corrected by the integer ambiguity with the integer ambiguity resolution success in the differential satellite subset χ j , represents the position fixed solution corrected by the integer ambiguity with the integer ambiguity resolution failure corresponding to the integer ambiguity resolution failure event k in the differential satellite subset χ j , VAL represents the vertical alert limit, and k represents the k-th integer ambiguity resolution failure event (i.e., the integer ambiguity resolution failure event k).

[0042] Calculate and The methods are existing technical methods, that is, using the fixed integer ambiguity to correct the position floating point solution to obtain the position fixed solution. If the fixed and correct integer ambiguity is used for correction, the obtained is the position fixed solution. If it is corrected by using the fixed integer ambiguity, the fixed solution of the position can be obtained. This will not be elaborated here.

[0043] Combined with Equation (5), Equation (6) can be rearranged as

[0044]

[0045] In Equation (7), ο(*) represents the infinitesimal of *, which can be ignored in practice; IR req represents the preset integrity risk index, lf represents the loss factor, and k max represents the number of integer ambiguity resolution failure events obtained after simplification. The meanings of other parameters can be seen in Equation (6), and will not be repeated here.

[0046] According to the statistical characteristics of the vertical position correction solution, Equation (7) can be transformed into

[0047]

[0048] In Equation (8), although the relevant parameters have been described above, for the sake of clarity, they are repeated here as follows: represents the integrity risk of the differential satellite subset χ j ; represents the probability of successful integer ambiguity resolution of the differential satellite subset χ j ; represents the probability of integer ambiguity resolution failure corresponding to the integer ambiguity resolution failure event k of the differential satellite subset χ j , where k max represents the number of integer ambiguity resolution failure events obtained after simplification, Ф(x) represents the cumulative probability density function of the standard normal distribution, VAL represents the vertical warning limit, and χ j represents the differential satellite subset, represents the fixed solution of the position corrected by using the integer ambiguity, k represents the kth integer ambiguity resolution failure event (i.e., the integer ambiguity resolution failure event k), represents the fixed solution of the position corrected by using the integer ambiguity resolution failure corresponding to the integer ambiguity resolution failure event k in the differential satellite subset χ j , ο(*) represents the infinitesimal of *, and IR req represents the preset integrity risk index, lf represents the loss factor, E(*) represents the mean operation, and D(*) represents the variance operation, represents the position solution variance calculated by the differential satellite subset χ j when the integer ambiguity is fixed correctly, represents the position solution variance calculated by the differential satellite subset χ jCalculated position solution variance.

[0049] This step S4) gives a method for calculating the integrity risk of all differential satellite subsets, as shown in Equation (8), which provides a theoretical basis for selecting the best differential satellite subset.

[0050] Step S5) selects the differential satellite subset with the lowest integrity risk based on the minimum integrity risk criterion.

[0051] According to Equation (8), the integrity risk corresponding to each differential satellite subset can be calculated. The present invention selects the available differential satellite subset with the lowest integrity risk based on the minimum integrity risk criterion. The specific method is as follows.

[0052]

[0053] In Equation (9), χ bc represents the differential satellite subset with the lowest integrity risk, argmin(*) represents obtaining the parameter that makes the function reach the minimum value, represents the integrity risk of the differential satellite subset χ j N sub represents the number of differential satellite subsets, then represents obtaining the differential satellite subset with the lowest integrity risk in the set of differential satellite subsets with the number of N sub χ represents the differential satellite subset with the lowest integrity risk, and χ j represents the differential satellite subset.

[0054] The differential satellite subset selected based on this step has the minimum integrity risk, which can assist users to achieve high-precision and high-reliability navigation and positioning.

[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 pertains, 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 multi-receiver differential satellite set selection method for carrier phase coordinated differential, comprising: Step S1) performing real-time differential positioning of carrier phase according to differential observations of multiple reference receivers and original observations of a single reference receiver, and generating all differential satellite subsets based on a multiple hypothesis solution separation method; Step S2) calculating the probability of successful integer ambiguity resolution and the probability of failed integer ambiguity resolution for each differential satellite subset according to the statistical characteristics of the integer ambiguity floating point solution; Step S3) comparing a preset integrity risk index with the obtained probability of integer ambiguity resolution failure, excluding integer ambiguity resolution failure events whose probability of integer ambiguity resolution failure is less than the product of the preset integrity risk index and the loss factor, and simplifying the number of integer ambiguity resolution failure events to a finite number; Step S4) using the vertical warning limit as the detection threshold, constructing a method for calculating the integrity risk of the differential satellite subset based on the calculation method of the probability of successful integer ambiguity resolution and the probability of failed integer ambiguity resolution, thereby calculating the integrity risk of all differential satellite subsets; Step S5) Based on the minimum integrity risk criterion, a differential satellite subset with the lowest integrity risk is selected.

2. The multi-receiver differential satellite set selection method for carrier phase coordinated differential according to claim 1, wherein: In step S1, there are N differential satellites for providing real-time differential positioning of carrier phase, and the corresponding differential satellite set is expressed as: χ all ={SV1 SV2…SV i …SV N } (1) where χ all Indicates the full set of available differential satellites, SV i represents the index of available differential satellite i; The expression of all differential satellite subsets generated is: Where N sub represents the number of differential satellite subsets, C represents the combination operator, and N represents the number of available satellites.

3. The multi-receiver differential satellite set selection method for carrier phase coordinated differential according to claim 2, wherein: In step S2, the method for calculating the probability of successful integer ambiguity resolution of the differential satellite subset is: in, represents the differential satellite subset χ j The probability of successful integer ambiguity resolution is , П(*) represents the product symbol, n represents the differential satellite subset χ j The number of integer ambiguities, i represents the differential satellite subset χ j The satellite index in , Ф(x) represents the cumulative probability density function of the standard normal distribution, Denotes the use of differential satellite subset χ j The satellite index number obtained from the observation is SV i The variance corresponding to the floating point solution of the satellite's integer ambiguity; The method for calculating the probability of integer ambiguity resolution failure corresponding to integer ambiguity resolution failure event k in the differential satellite subset is: in, represents the differential satellite subset χ j The probability of integer ambiguity resolution failure corresponding to the integer ambiguity resolution failure event k is: k represents the kth integer ambiguity resolution failure event, П(*) represents the product symbol, and n represents the differential satellite subset χ j The number of integer ambiguities, i represents the differential satellite subset χ j The satellite index in , Ф(x) represents the cumulative probability density function of the standard normal distribution, f k represents the fault unit vector corresponding to the integer ambiguity resolution failure event k, Δz k represents the integer ambiguity deviation amplitude corresponding to the integer ambiguity resolution failure event k, Denotes the use of differential satellite subset χ j The satellite index number obtained from the observation is SV i The variance corresponding to the floating-point solution of the satellite's integer ambiguity.

4. The multi-receiver differential satellite set selection method for carrier phase coordinated differential according to claim 3, wherein: In step S3, the method of reducing the number of integer ambiguity resolution failure events to a finite number is: in represents the simplified differential satellite subset χ j The finite number of integer ambiguity resolution failure events under , represents the differential satellite subset χ j The probability of integer ambiguity resolution failure corresponding to the integer ambiguity resolution failure event k; k represents the kth integer ambiguity resolution failure event, IR req represents the preset integrity risk index, lf represents the loss factor, and Z represents all integers; Use k max Represents the number of integer ambiguity resolution failure events after simplification.

5. The multi-receiver differential satellite set selection method for carrier phase coordinated differential according to claim 4, wherein: In step S4, the method for calculating the integrity risk of all differential satellite subsets is: in represents the differential satellite subset χ j The integrity risk represents the differential satellite subset χ j The probability of successful integer ambiguity resolution is: represents the differential satellite subset χ j The probability of integer ambiguity resolution failure corresponding to the integer ambiguity resolution failure event k, k max represents the number of integer ambiguity resolution failure events after simplification, Ф(x) represents the cumulative probability density function of the standard normal distribution, VAL represents the vertical alarm limit, χ j represents the differential satellite subset, represents the position fix solution using integer ambiguity correction, k represents the kth integer ambiguity resolution failure event, Denotes the use of differential satellite subset χ j The position fixed solution of the integer ambiguity correction corresponding to the integer ambiguity resolution failure event k in the integer ambiguity resolution failure, ο(*) represents the infinitesimal of *, IR req represents the preset integrity risk index, lf represents the loss factor, E(*) represents the mean operation, Indicates that the integer ambiguity is fixed correctly by the differential satellite subset χ j The variance of the position solution is calculated, represents the differential satellite subset x under the integer ambiguity resolution failure event k j The variance of the solved position solution.

6. The multi-receiver differential satellite set selection method for carrier phase coordinated differential according to claim 5, wherein: In step S5, the method of selecting the differential satellite subset with the lowest integrity risk is: where χ bc represents the differential satellite subset with the lowest integrity risk, argmin(*) represents the parameter that makes the function achieve the minimum value, represents the differential satellite subset χ j The integrity risk, N sub represents the number of differential satellite subsets, then Indicates that the number is N sub The integrity risk is obtained from the set of differential satellite subsets The lowest difference satellite subset.

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