Horizontal exclusion level calculation method suitable for GNSS single-frequency single-constellation architecture

Abstract

The invention discloses a horizontal exclusion level calculation method suitable for a GNSS single-frequency single-constellation architecture, which aims at the GNSS single-frequency single-constellation architecture, analyzes and establishes a signal propagation path full-link error model, and calculates a horizontal exclusion level of the GNSS single-frequency single-constellation architecture on the basis of weighted least squares, hypothesis testing and biased estimation theories. And designing a horizontal exclusion level calculation method based on geometric factors and adaptive noise expansion so as to improve the integrity guarantee capability. According to the method, the uncertainty of the single-frequency ionosphere and the parameter self-adaption and availability limitation in the flight stage (ocean area / air route / terminal / non-precision approach) are considered, and the availability in the SFSC environment can be improved while the integrity and the safety are ensured.

Description

Technical Field

[0001] This invention belongs to the field of Global Navigation Satellite System (GNSS) integrity research in civil aviation, and particularly relates to a horizontal exclusion level calculation method applicable to GNSS single-frequency single-constellation architecture. Background Technology

[0002] Satellite navigation signals have low power and are very fragile, making them susceptible to intentional or unintentional interference from outside the system. This can lead to reduced accuracy or even loss of navigation and positioning capabilities. In the civil aviation sector, where safety requirements are the highest, accurate assessments are needed based on the aircraft's different flight phases to provide high-precision, highly reliable, and continuous navigation and positioning performance.

[0003] The International Civil Aviation Organization (ICAO) clearly defines the performance requirements that GNSS should meet in its GNSS standards and recommended practices, including accuracy, integrity, continuity, and availability. The availability of a navigation system refers to its ability to provide the required functions and performance during its intended operation, reflecting its capacity to provide available services within a specified effective area. The BeiDou Navigation Satellite System will be gradually incorporated into the civil aviation GNSS standards framework, becoming one of the core constellations. A detailed and careful assessment of its global service capabilities is necessary, especially parameters such as horizontal protection level and horizontal exclusion level.

[0004] Although the DO-229 standard provides design requirements for integrity monitoring of GPS single-frequency satellite-based augmentation systems (SBAS), and the DO-401 standard provides integrity monitoring requirements based on dual-frequency SBAS, which can provide vertical guidance and even Class I precision approaches, due to various factors such as regional development differences, accidental or malicious navigation signal interference, service levels, and costs, SBAS and other augmentation systems cannot fully cover the entire flight phase. Under necessary or limited conditions, airborne navigation methods will eventually be downgraded to receiver autonomous integrity monitoring. In addition, in the field of low-altitude general aviation, due to cost, energy consumption, or equipment limitations, airborne platforms such as general aviation or UAVs may use single-frequency single-constellation receivers and are not equipped with high-performance inertial navigation units, especially relying on the autonomous integrity monitoring capabilities of GNSS navigation receivers. Therefore, there is still a need and importance to study the integrity monitoring of GNSS single-frequency single-constellation. At this time, it is not only necessary to realize the ability to detect the occurrence of faults, but also to enable the equipment to identify and eliminate specific faulty satellites through algorithms, so as to improve and ensure the accuracy, integrity and availability of navigation and positioning, and provide better navigation and guidance capabilities for aircraft. Summary of the Invention

[0005] To address the aforementioned issues, this invention provides a horizontal exclusion level calculation method applicable to GNSS single-frequency single-constellation architecture.

[0006] The present invention provides a horizontal exclusion level calculation method applicable to GNSS single-frequency single-constellation architecture, comprising the following steps:

[0007] Step 1: Construct the satellite position navigation solution equation.

[0008] Assume there are N available satellites, and the satellite set is M = {M1, M2, ..., M}. N}, each satellite M i The azimuth and elevation angles are respectively A i and E i The unit is radians.

[0009] The satellite position navigation solution equation is as follows:

[0010]

[0011]

[0012]

[0013] In the formula, x is a linearized four-dimensional position vector (north, east, day, and time), and y is an N-dimensional vector corresponding to each satellite, which contains the original pseudo-distance measurement value minus the expected distance value based on the satellite position and the user position.

[0014] The weighted least squares solution is:

[0015]

[0016] Right now:

[0017]

[0018] Let S = I - GA, where S is the projection matrix.

[0019] G is the satellite observation matrix. It is its transpose matrix; I is the N-dimensional identity matrix, that is, the diagonal is 1 and the rest are all 0; It is the least squares solution obtained through iterative calculation.

[0020] Step 2: Estimate the pseudorange measurement error of each available satellite to calculate the weight matrix.

[0021] When calculating the position using the weighted least squares method, the pseudorange measurement error estimation formula for each available satellite is as follows:

[0022]

[0023] Therefore, the diagonal elements of the weight matrix are:

[0024]

[0025] Item 1: Equivalent Measurement Accuracy of Satellite Ephemeris and Clock Bias (URA) i Set to a fixed value.

[0026] Item 2: Evaluate ionospheric correction errors using a model .

[0027]

[0028] Where c represents the speed of light in a vacuum; T iono Correction for ionospheric errors calculated by the model.

[0029] The projection function of the ionosphere at the puncture point F pp The calculation formula is as follows:

[0030]

[0031] Where Re is the average radius of the Earth; H ion This represents the height of the ionosphere.

[0032] τ vert This is the ionospheric accuracy assessment data for the vertical puncture point, in meters, calculated using the following formula:

[0033]

[0034] Among them, geomagnetic latitude ϕ m Calculated based on the ICD of each GNSS system.

[0035] Item 3: Assess the propagation error of navigation signals in the atmosphere. for:

[0036]

[0037] Considering the upper limits of the errors of measurement noise and code deviation, the formula is as follows:

[0038]

[0039] Multipath measurement error is calculated based on the following model:

[0040]

[0041] Item 4: Evaluate tropospheric error σ i,tropo The estimation formula is:

[0042]

[0043] in It is 0.12 meters; .

[0044] Step 3: Calculate M for each satellite i The maximum slope and the current satellite set M={M1,M2,⋯,M N Horizontal protection level:

[0045]

[0046]

[0047]

[0048] The subscripts 1i, 2i, and ii indicate taking the elements in the corresponding row and column of the matrix.

[0049] Wherein, λ is based on the civil aviation risk probability requirement P fa and P md It is calculated using the following formula.

[0050]

[0051]

[0052] In the formula, Let represent the probability density function of a chi-square distribution with n-4 degrees of freedom. Let T represent the probability density function of a non-centralized chi-square distribution with n-4 degrees of freedom and a non-centrality parameter λ. n This is a critical value that satisfies the condition, also known as the quantile of the chi-square distribution.

[0053] Step 4: Calculate the level of exclusion.

[0054] First, consider the current satellite M = {M1, M2, ..., M}. N By successively excluding any satellite from the set, we obtain N satellite subsets. .

[0055]

[0056] Based on steps 1-3, for any subset M ej They all get an HPL ej .

[0057] The horizontal exclusion level corresponding to the set M of all satellites is:

[0058]

[0059] Furthermore, in step 2, URA i The value is 5.7.

[0060] Furthermore, in step 3, for the non-precision approach phase, P fa =3.33×10 -7 P md =10 -3 .

[0061] The beneficial technical effects of this invention are as follows:

[0062] Based on airworthiness standard risk probabilities and integrity capability requirements, this invention analyzes and establishes a full-link error model for the signal propagation path in a single-frequency, single-constellation GNSS architecture. Based on weighted least squares, hypothesis testing, and biased estimation theory, a horizontal exclusion-level calculation method based on geometric factors and adaptive noise expansion is designed to improve integrity assurance capabilities. The system takes into account single-frequency ionospheric uncertainties, adaptive parameters during flight phases (ocean area / en-way / terminal / non-precision approach), and availability constraints, thus improving availability in SFSC environments while ensuring integrity and safety. Attached Figure Description

[0063] Figure 1 This is a flowchart of the horizontal exclusion level calculation method applicable to GNSS single-frequency single-constellation architecture. Detailed Implementation

[0064] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0065] The present invention provides a horizontal exclusion level calculation method applicable to GNSS single-frequency single-constellation architecture, comprising the following steps:

[0066] Step 1: Construct the satellite position navigation solution equation.

[0067] Assume there are N available satellites, and the satellite set is M = {M1, M2, ..., M}. N}, each satellite M i The azimuth and elevation angles are respectively A i and E i The unit is radians.

[0068] The satellite position navigation solution equation is as follows:

[0069]

[0070]

[0071]

[0072] The weighted least squares solution is:

[0073]

[0074] Right now:

[0075]

[0076] Let S = I - GA, where S is the projection matrix.

[0077] Step 2: Estimate the pseudorange measurement error of each available satellite to calculate the weight matrix.

[0078] When calculating the position using the weighted least squares method, the pseudorange measurement error estimation formula for each available satellite is as follows:

[0079]

[0080] Therefore, the diagonal elements of the weight matrix are:

[0081]

[0082] Item 1: Equivalent Measurement Accuracy of Satellite Ephemeris and Clock Bias (URA) i Set to a fixed value. Normally, URA... i The value is 5.7.

[0083] Item 2: Evaluate ionospheric correction errors using a model .

[0084]

[0085] Where c represents the speed of light in a vacuum, with a value of 299,792,458 meters per second; T iono Ionospheric error correction for model calculations (in seconds).

[0086] The projection function of the ionosphere at the puncture point F pp The calculation formula is as follows:

[0087]

[0088] Where Re is the average radius of the Earth; H ion This represents the height of the ionosphere.

[0089] τ vert This is the ionospheric accuracy assessment data for the vertical puncture point, in meters, calculated using the following formula:

[0090]

[0091] Among them, geomagnetic latitude ϕ m Calculated based on the ICD of each GNSS system.

[0092] Item 3: Assess the propagation error of navigation signals in the atmosphere. for:

[0093]

[0094] Considering the upper limits of the errors of measurement noise and code deviation, the formula is as follows:

[0095]

[0096] Multipath measurement error is calculated based on the following model:

[0097]

[0098] Item 4: Evaluate tropospheric error σ i,tropo The estimation formula is:

[0099]

[0100] in It is 0.12 meters; .

[0101] Step 3: Calculate M for each satellite i The maximum slope and the current satellite set M={M1,M2,⋯,M N Horizontal protection level:

[0102]

[0103]

[0104]

[0105] The subscripts 1i, 2i, and ii indicate taking the elements in the corresponding row and column of the matrix.

[0106] Wherein, λ is based on the civil aviation risk probability requirement P fa and P md It is calculated using the following formula.

[0107]

[0108]

[0109] For the non-precision approach phase, P fa =3.33×10 -7 P md =10 -3 .

[0110] Step 4: Calculate the level of exclusion.

[0111] First, consider the current satellite M = {M1, M2, ..., M}. N By successively excluding any satellite from the set, we obtain N satellite subsets. .

[0112]

[0113] Based on steps 1-3, for any subset M ej They all get an HPL ej .

[0114] The horizontal exclusion level corresponding to the set M of all satellites is:

[0115]

[0116] Although the illustrative specific embodiments of the present invention have been described above to enable those skilled in the art to understand the invention, the invention is not limited to the scope of the specific embodiments. For those skilled in the art, all inventions utilizing the concept of the present invention are protected as long as various variations are within the spirit and scope of the invention as defined and determined by the appended claims.

Claims

1. A horizontal exclusion level calculation method applicable to GNSS single-frequency single-constellation architecture, characterized in that, Includes the following steps: Step 1: Construct the satellite position navigation solution equations; Assume there are N available satellites, and the satellite set is M = {M1, M2, ..., M}. N }, each satellite M i The azimuth and elevation angles are respectively A i and E i The unit is radians; The satellite position navigation solution equation is as follows: ； ； ； In the formula, x is a linearized four-dimensional position vector, and y is an N-dimensional vector corresponding to each satellite, which contains the original pseudo-distance measurement value minus the expected distance value based on the satellite position and the user position; The weighted least squares solution is: ； Right now: ； Let S = I - GA, where S is the projection matrix; G is the satellite observation matrix. It is its transpose matrix; I is the N-dimensional identity matrix, that is, the diagonal is 1 and the rest are all 0; It is the least squares solution obtained through iterative calculation; Step 2: Estimate the pseudorange measurement error of each available satellite to calculate the weight matrix; When calculating the position using the weighted least squares method, the pseudorange measurement error estimation formula for each available satellite is as follows: ； Therefore, the diagonal elements of the weight matrix are: ； Item 1: Equivalent Measurement Accuracy of Satellite Ephemeris and Clock Bias (URA) i Set to a fixed value; Item 2: Evaluate ionospheric correction errors using a model ; ； Where c represents the speed of light in a vacuum; T iono Correction for ionospheric errors calculated by the model; The projection function of the ionosphere at the puncture point F pp The calculation formula is as follows: ； Where Re is the average radius of the Earth; H ion The height of the ionosphere thin layer; τ vert This is the ionospheric accuracy assessment data for the vertical puncture point, in meters, calculated using the following formula: ； Among them, geomagnetic latitude ϕ m Calculated based on ICD of each GNSS system; Item 3: Assess the propagation error of navigation signals in the atmosphere. for: ； Considering the upper limits of the errors of measurement noise and code deviation, the formula is as follows: ； Multipath measurement error is calculated based on the following model: ； Item 4: Evaluate tropospheric error σ i,tropo The estimation formula is: ； in It is 0.12 meters; ; Step 3: Calculate M for each satellite i The maximum slope and the current satellite set M={M1,M2,⋯,M N Horizontal protection level: ； ； ； The subscripts 1i, 2i, and ii indicate taking the elements in the corresponding row and column of the matrix; Wherein, λ is based on the civil aviation risk probability requirement P fa and P md It can be calculated using the following formula; ； ； In the formula, Let represent the probability density function of a chi-square distribution with n-4 degrees of freedom. Let T represent the probability density function of a non-centralized chi-square distribution with n-4 degrees of freedom and a non-centrality parameter λ. n This is a critical value that satisfies the condition, also known as the quantile of the chi-square distribution; Step 4: Calculate the level of exclusion; First, consider the current satellite M = {M1, M2, ..., M}. N By successively excluding any satellite from the set, we obtain N satellite subsets. ; ； Based on steps 1-3, for any subset M ej They all get an HPL ej ; The horizontal exclusion level corresponding to the set M of all satellites is: 。 2. The horizontal exclusion level calculation method applicable to GNSS single-frequency single-constellation architecture according to claim 1, characterized in that, In step 2, URA i The value is 5.

7.

3. The horizontal exclusion level calculation method applicable to GNSS single-frequency single-constellation architecture according to claim 1, characterized in that, In step 3, for the non-precision approach phase, P fa =3.33×10 -7 P md =10 -3 .

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