A method for positioning and precision evaluation of aircraft three-dimensional coordinates under land-based navigation mode

Abstract

The application relates to the technical field of aircraft navigation positioning, and discloses a three-dimensional coordinate positioning and precision evaluation method for an aircraft under a land-based navigation mode. The method first constructs an oblique-axis equidistant cutting azimuth projection coordinate direct calculation algorithm, converts longitude and latitude coordinates and elevation in a navigation station geodetic coordinate system into projection coordinates in a region-independent coordinate system; then, based on the minimum principle of the weighted sum of squares of measurement residuals, establishes a positioning point coordinate component correction number calculation model according to the magnetic differences and measurement values of the navigation stations to obtain optimal estimates of the positioning point coordinates; subsequently, the optimal estimates are converted into longitude, latitude and elevation in the geodetic coordinate system through a projection coordinate inverse calculation algorithm; finally, a positioning precision evaluation algorithm is constructed based on RNP operation rules to calculate the lateral positioning deviation of the aircraft within a 95% confidence interval. The positioning precision and operation reliability of the aircraft under the land-based navigation mode are effectively improved through the optimal estimates of the positioning point coordinates and the positioning precision evaluation.

Description

Technical Field

[0001] This invention relates to the field of aircraft navigation and positioning technology, specifically a method for three-dimensional coordinate positioning and accuracy assessment of aircraft based on VOR / DME (Very High Frequency Omnidirectional Beacon / Distance Meter) land-based navigation stations to achieve RNP (Required Navigation Performance) operation. Background Technology

[0002] Aircraft navigation and positioning accuracy and reliability are key elements for the safe, efficient, and orderly operation of civil aviation. Performance-based navigation (PBN) is an emerging navigation method in the aviation field. One of its navigation specifications, Required Navigation Performance (RNP), enables aircraft to navigate along any planned flight path within the effective coverage area of ​​navigation facilities, and provides real-time monitoring and alerting capabilities for horizontal positioning accuracy.

[0003] As an important land-based facility for positioning and guiding aircraft, VOR / DME (Very High Frequency Omnidirectional Beacon / Distance Meter) has limitations such as low accuracy in horizontal azimuth and slant range measurement, and the inability to obtain horizontal distance measurements to perform rigorous calculations of positioning point coordinates.

[0004] Existing traditional land-based navigation and positioning algorithms have the following drawbacks: 1. They approximate the Earth as a perfect sphere with a constant radius for coordinate projection calculations, resulting in discrepancies with the known latitude and longitude coordinates of the navigation station based on the geodetic coordinate system; 2. They approximate the slant range measurements of VOR / DME land-based navigation stations as horizontal distances in the positioning coordinate calculation, introducing systematic errors; 3. They lack the ability to calculate the lateral positioning deviation of aircraft within the 95% confidence interval required by RNP operating rules. Therefore, current land-based navigation and positioning algorithms have not yet achieved high-precision and rigorous solution of positioning point coordinates and positioning accuracy calculations, only possessing RNAV (Area Navigation) operation capabilities and cannot independently support RNP operation. Summary of the Invention

[0005] The purpose of this invention is to provide a method for three-dimensional coordinate positioning and accuracy evaluation of aircraft under land-based navigation, so as to solve the technical problems that the existing positioning algorithms under land-based navigation have low solution accuracy and do not have the positioning accuracy calculation capability required by the RNP operating specifications.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A method for three-dimensional coordinate positioning and accuracy evaluation of aircraft under land-based navigation includes the following steps: S1: Construct an oblique axis equidistant tangential projection coordinate forward calculation algorithm to convert the latitude and longitude coordinates and elevation of the land-based navigation station based on the geodetic coordinate system into the projected coordinates of the regional independent coordinate system; S2: Construct an algorithm to calculate the starting coordinates of the positioning point, obtain the measurement data and magnetic difference of each navigation station, and calculate the starting coordinates of the positioning point; S3: Based on the starting coordinates of the positioning point and the relevant measurement values ​​of the navigation station, construct a matrix-form expression for the measurement value residual vector; S4: Calculate and construct the measurement value weight matrix based on the accuracy characteristics of the navigation station's horizontal azimuth and slant range measurements; S5: Based on the principle of minimizing the weighted sum of squares of the residuals of the measured values, establish a calculation model for the correction of the coordinate components of the positioning point, and calculate the correction and estimated coordinates of the positioning point. S6: The optimal estimated coordinates of the positioning point are obtained by using an iterative calculation method; S7: Construct an algorithm for back-calculation of oblique axis equidistant tangential projection coordinates, and convert the optimal estimated coordinates of the positioning point into latitude and longitude coordinates and elevation in the geodetic coordinate system; S8: Based on the RNP operating rules, construct a positioning accuracy assessment algorithm to calculate the lateral positioning deviation of the aircraft within the 95% confidence interval.

[0007] As a further aspect of the present invention, the weight is closely related to the measurement accuracy, reflecting the relative importance and reliability of each measurement value in the process of optimal estimation calculation.

[0008] As a further aspect of the present invention: the residual is the difference between the measured value and the optimal estimate of the computational model.

[0009] As a further aspect of the present invention: a forward calculation algorithm for oblique axis equidistant tangential projection coordinates is constructed, comprising: A method for calculating the latitude and longitude coordinates of the projection center is established to determine the latitude and longitude coordinates of the projection center in the geodetic coordinate system; On the reference ellipsoid corresponding to the geodetic coordinate system, construct a tangent plane with the projection center as the tangent point, and use this tangent plane as the projection plane; On the projection plane, with the projection center as the origin O, the X-axis passes through point O and points north of the meridian, the Z-axis passes through point O and is perpendicular to the projection plane, pointing outward from the reference ellipsoid, and the Y-axis, together with the X-axis and Z-axis, forms a left-handed spatial rectangular coordinate system, which is the regional independent coordinate system. On the projection plane, the distance along the meridian or parallel is equal to the actual distance in the corresponding direction on the reference ellipsoid, with no length projection distortion; The latitude, longitude, and elevation coordinates of the land-based navigation station based on the geodetic coordinate system are obtained, and the projected coordinates of the land-based navigation station in the regional independent coordinate system are calculated.

[0010] As a further aspect of the present invention: a method for calculating the latitude and longitude coordinates of the projection center is constructed, comprising: Determine the number of land-based navigation stations participating in the coordinate positioning calculation, and obtain the latitude and longitude coordinates of each land-based navigation station based on the geodetic coordinate system; Calculate the arithmetic mean of the minimum and maximum longitude coordinates of each land-based navigation station, and use it as the longitude coordinate of the projection center; Calculate the arithmetic mean of the minimum and maximum latitude coordinates of each land-based navigation station to obtain the latitude coordinates of the projection center.

[0011] As a further aspect of the present invention: calculating the projected coordinates of the land-based navigation station in a regional independent coordinate system includes: Based on the semi-major axis length a and semi-minor axis length b of the reference ellipsoid, the first eccentricity e of the reference ellipsoid is calculated. Obtain the latitude, longitude, and elevation (λ) coordinates of the land-based navigation station in the geodetic coordinate system. i , φ i , h i ),in, i Refers to the first i Land-based navigation stations; The latitude and longitude coordinates (λ) of the projection center in the independent coordinate system of the area where the navigation station is located are obtained using the projection center latitude and longitude coordinate calculation method. O , φ O ); Based on the latitude and longitude coordinates of the projection center and the latitude, longitude coordinates and elevation of the land-based navigation station, the projected coordinates of the land-based navigation station in the regional independent coordinate system are calculated. The formula for calculating the projected coordinates of a land-based navigation station in a regional independent coordinate system is as follows: ,in, Let be the latitude, longitude, latitude, and elevation of the i-th land-based navigation station. Let be the projected coordinates of the i-th land-based navigation station in the regional independent coordinate system, 'a' be the length of the semi-major axis of the reference ellipsoid, and 'e' be the first eccentricity of the reference ellipsoid, calculated as follows: .

[0012] As a further aspect of the present invention: constructing an algorithm for calculating the starting coordinates of the positioning point, including: obtaining the magnetic azimuth and slant distance measurements of each land-based navigation station and the local magnetic difference, and calculating the starting coordinates of the positioning point in the regional independent coordinate system; ,in, Let n be the starting coordinates of the positioning point, and n be the number of land-based navigation stations participating in the positioning calculation. Let be the coordinates of the i-th land-based navigation station in the regional independent coordinate system. This is the true azimuth of the aircraft, and , Let be the measured magnetic azimuth angle of the aircraft at the positioning point by the i-th land-based navigation station. Let be the magnetic difference at the location of the i-th navigation station. Let be the slant distance measurement value of the i-th navigation station to the positioning point.

[0013] As a further aspect of the present invention: constructing a matrix-form expression for the measurement residual vector includes: enumerating the general form of the measurement residual expression based on the starting coordinates of the positioning point and the relevant measurement values ​​of the navigation station; expanding the above expression using a Maclaurin series and retaining the first two terms to obtain a linearized residual expression; and constructing a matrix-form expression for the residual vector based on the linearized residual expression; wherein: The general form of the expression for the residual of the measured value is:

[0014] in, , These are the residuals of the horizontal azimuth and slant range measurements of the i-th land-based navigation station, respectively. , , Correction value for the coordinates of the positioning point; Based on the general form of the measurement residual expression using the Maclaurin series expansion, retaining the first two terms of the expansion, the resulting linearized expression is:

[0015] in, The approximate slant distance between the positioning point and navigation station i is calculated based on the starting coordinates of the positioning point: ; Based on the linearized residual expression of the measured values ​​described above, a matrix-form residual vector expression is constructed: ; in, The residual vector of measured values: A is the coefficient matrix; Correction vector for coordinate values: c is a vector of constant terms.

[0016] As a further aspect of the present invention: based on the accuracy characteristics of the horizontal azimuth and slant range measurements of navigation stations, a measurement value weight matrix is ​​calculated and constructed, including: calculating the weights of the horizontal azimuth and slant range measurements of each land-based navigation station according to the measurement accuracy characteristics of the land-based navigation stations (VOR / DME); and constructing a weight matrix based on the measurement value weights. The weighting formula for the horizontal azimuth and slant range measurements of each navigation station is as follows:

[0017] in, , These are the weights of the horizontal azimuth and slant range measurements of the i-th navigation station, respectively; NM is the unit: nautical mile.

[0018] Construct a measurement value weight matrix based on the aforementioned weight values:

[0019] As a further aspect of the present invention: based on the weighted sum of squares of the residuals of the measured values ​​( Based on the principle of minimum, an algorithm for solving the correction vector of the coordinate components of the positioning point is constructed to calculate the correction of the coordinate components of the positioning point, thereby obtaining the estimated coordinates of the positioning point.

[0020] The formula for calculating the correction vector of the positioning point coordinate components is as follows: ,in, Correction vector for the coordinate values ​​of the positioning point: , The coefficient matrix in the residual vector expression. Let P be the transpose of the coefficient matrix, and let P be the measurement weight matrix.

[0021] Based on the correction values ​​of the positioning point coordinates, the estimated coordinates (x, y, z) of the positioning point are obtained:

[0022] As a further aspect of this invention: the optimal estimated coordinates of the positioning point are calculated using an iterative calculation method, including: obtaining coordinate value corrections based on the starting coordinates of the positioning point, thereby obtaining the estimated coordinates of the positioning point; incorporating the estimated coordinates of the positioning point as the new starting coordinates of the positioning point into the above scheme; constructing a matrix-form expression for the residual vector of the measurement values ​​based on the starting coordinates of the positioning point and the relevant measurement values ​​of the navigation station; calculating and constructing a measurement value weight matrix based on the accuracy characteristics of the horizontal azimuth and slant range measurements of the navigation station; establishing a calculation model for the corrections of the positioning point coordinate components based on the principle of minimizing the weighted sum of squares of the measurement value residuals, and calculating the corrections and estimated coordinates of the positioning point; performing iterative calculations using an iterative calculation method until the corrections of the coordinate values ​​satisfy the iterative convergence condition; at this point, the obtained estimated coordinates of the positioning point are the optimal estimated values. The estimated coordinates of the positioning point are obtained based on the starting coordinates of the positioning point: , where j represents the j-th calculation result in the iteration process; Use the coordinates of the positioning point in this calculation as the starting coordinates of the new positioning point: ; The new starting coordinates of the positioning point are incorporated into steps S3 to S6 for iterative calculation until the coordinate value correction satisfies the convergence condition, thus obtaining the optimal estimated coordinates of the positioning point. .in, This represents the coordinate estimation result when the convergence condition is met after the m-th iteration.

[0023] In step S3, during the linearization of the general expression for the measured residuals, only the first two terms of the Maclaurin series expansion are retained. This is done when the coordinate component correction vector... When the elements in the calculation are large, it will cause a loss of calculation accuracy. Using iterative calculation methods can reduce the accuracy loss caused by linearization calculation.

[0024] As a further aspect of this invention: in the iterative calculation method used to estimate the coordinates of the positioning point, the convergence condition is: ,in, This is the convergence threshold for the coordinate component corrections, which is a small value determined based on the required computational accuracy.

[0025] As a further aspect of this invention: A reverse calculation algorithm for oblique axis equidistant tangent projection coordinates is constructed to convert the optimal estimated coordinates of the positioning point into latitude, longitude, and elevation coordinates in a geodetic coordinate system, including: The approximate latitude of the positioning point is calculated based on its ordinate in the regional independent coordinate system, the latitude of its projection center, and the ellipsoid parameters. The deviation of the ordinate in the regional independent coordinate system is calculated based on this approximate latitude, thus obtaining a corrected latitude value. This corrected latitude value is then used as a new approximate latitude value for iterative calculation until the iterative convergence condition is met, yielding the latitude of the positioning point in the geodetic coordinate system. Finally, the longitude and elevation of the positioning point in the geodetic coordinate system are calculated based on its abscissa and ordinate in the regional independent coordinate system, the longitude of its projection center, and the reference ellipsoid parameters. Specifically, the latitude, longitude, and elevation of the positioning point in the geodetic coordinate system are calculated based on the coordinates of the positioning point in the regional independent coordinate system, the latitude and longitude of the projection center, and the ellipsoid parameters, including: Based on the optimal estimate of the location point's coordinates, the approximate latitude of the location point in the geodetic coordinate system is calculated using the following formula: ;in, These are approximate latitude coordinates of the location point. Here, is the latitude of the projection center, 'a' is the length of the semi-major axis of the reference ellipsoid in the geodetic coordinate system, and 'e' is the first eccentricity. The optimal estimate for the ordinate of the positioning point; Calculate the deviation of the ordinate in the independent coordinate system of the region based on the approximate latitude coordinates of the positioning point: ;in, For the firstk The approximate latitude value obtained from the next iteration. k=0,1,2,…… ; This refers to the deviation of the ordinate in a regionally independent coordinate system, i.e., based on the latitude approximation. The difference between the calculated ordinate in the regional independent coordinate system and the actual ordinate; Calculate the latitude coordinate correction value in the geodetic coordinate system based on the vertical coordinate deviation: ,in, This is a latitude correction value; Correct latitude coordinates As a new approximation of latitude coordinates, the above scheme is incorporated: the ordinate deviation in the independent coordinate system of the calculation area is updated based on the new approximation of latitude coordinates; the corrected latitude coordinates in the geodetic coordinate system are calculated based on the ordinate deviation and iterative calculation is performed until the iterative convergence condition is met. ,in, The deviation of the ordinate in the region-independent coordinate system. The ordinate deviation convergence threshold is used as the reference value. At this point, the calculated result... That is, the optimal estimate of the coordinates of the positioning point is the latitude in the geodetic coordinate system. ; The optimal estimate of the location point's coordinates, including its longitude and elevation in the geodetic coordinate system, is calculated using the following formula: ,in, , , These represent the optimal estimated coordinates of the positioning point in the geodetic coordinate system, specifically the latitude, longitude, and elevation. , These are the optimal estimates for the x-coordinate and y-coordinate of the positioning point, respectively. The longitude of the projection center. a The length of the semi-major axis of the reference ellipsoid in the geodetic coordinate system. e This is the first eccentricity.

[0026] As a further aspect of the present invention: a positioning accuracy assessment algorithm is constructed to calculate the lateral positioning deviation of the aircraft within a 95% confidence interval, including: calculating the unit weight variance and covariance matrix; calculating the positioning point accuracy distribution ellipse parameters; and calculating the lateral positioning deviation of the aircraft within a 95% confidence interval.

[0027] The formula for calculating unit weighted variance is as follows:

[0028] in, The variance is the unit weight. Let P be the residual vector of the measured values ​​mentioned above, where P is the weight matrix of the measured values ​​and n is the number of navigation stations involved in solving the coordinates of the positioning point. The covariance matrix is ​​calculated based on the unit weighted variance, using the following formula:

[0029] Among them, covariance matrix Its composition is as follows:

[0030] in, , , The variance of the corresponding coordinate components. , , The covariance between corresponding coordinate components; The formula for calculating the ellipse parameters of the positioning point accuracy distribution is as follows:

[0031] in, , These represent the positional error of the positioning point accuracy distribution ellipse along the major and minor semi-axis directions, respectively. The true azimuth of the major semi-axis of the ellipse for positioning point accuracy distribution.

[0032] Based on the ellipse parameters of the positioning point accuracy distribution, the formula for calculating the lateral positional error of the positioning point is as follows:

[0033] in, This represents the lateral positional error of the positioning point. True azimuth angle for guiding aircraft flight paths.

[0034] The formula for calculating the lateral positioning deviation of an aircraft within a 95% confidence interval is as follows:

[0035] Compared with the prior art, the beneficial effects of the present invention are: 1. This invention proposes a method for three-dimensional coordinate positioning and accuracy assessment of aircraft based on the principle of minimizing the weighted sum of squares of measurement residuals using the original measurement data from existing land-based navigation stations (VOR / DME). This method can further improve the accuracy of aircraft land-based navigation and positioning on the basis of existing technology, and effectively reduce positioning errors caused by factors such as navigation station position errors, measurement errors, and coordinate projection distortion.

[0036] 2. This invention overcomes the limitation of existing land-based navigation and positioning algorithms in assessing aircraft positioning accuracy. With the support of land-based navigation equipment, it can estimate the lateral positioning deviation of an aircraft within a 95% confidence interval, thereby adapting to RNP operating rules and application requirements and improving the safety and reliability of aircraft operation. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of the map projection principle in this invention; Figure 2 This is a first schematic diagram of the three-dimensional coordinate positioning calculation in this invention; Figure 3 This is a second schematic diagram of the three-dimensional coordinate positioning calculation in this invention; Figure 4 This is a schematic diagram of the ellipse calculation for the accuracy distribution of positioning points in this invention; Figure 5 This is a schematic diagram showing the positions of the aircraft and navigation stations in the simulation experiment verification of this invention; Figure 6 This is a flowchart of the method of the present invention. Detailed Implementation

[0038] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0039] Example: Based on a flight simulation platform, four VOR / DME stations in a certain area were selected as the source of land-based navigation and positioning data. Horizontal magnetic azimuth and slant range measurements were performed on aircraft flying along a certain route at different positions and altitudes. Then, the calculation method proposed in this invention was used to solve for the coordinates and positioning accuracy of the aircraft's positioning points. Finally, the calculation results were compared and analyzed with the results obtained by existing related calculation methods.

[0040] It should be noted that "World Geodetic System 1984" is a geodetic coordinate system established by the International Civil Aviation Organization (ICAO) as the coordinate benchmark uniformly adopted in the global civil aviation field. Its English name is World Geodetic System 1984, and its English abbreviation is WGS84.

[0041] Please see Figure 1 - Figure 6 This embodiment discloses a method for three-dimensional coordinate positioning and accuracy evaluation of aircraft under land-based navigation, including the following steps: S1: Construct an oblique axis equidistant tangent azimuth projection coordinate forward calculation algorithm to convert the latitude and longitude coordinates and elevation of the land-based navigation station based on the geodetic coordinate system into the projected coordinates of the regional independent coordinate system.

[0042] Specifically, in step S1, four VOR / DME land-based navigation stations with known latitude, longitude, and elevation coordinates in the WGS84 coordinate system are selected in a certain area; the latitude and longitude coordinates of the projection center are determined by the oblique axis equidistant tangent azimuth projection coordinate forward calculation algorithm; an area-independent coordinate system is established, and the latitude, longitude, and elevation coordinates of each land-based navigation station are converted into projected coordinates in the area-independent coordinate system (see Table 1 for relevant information of each land-based navigation station).

[0043] The algorithm for calculating the oblique axis equidistant tangent azimuth projection coordinates includes: 1) Determine the latitude and longitude coordinates of the projection center. The calculation formula is as follows: (1) in, , These are the longitude and latitude coordinates of the projection center, respectively, and n is the number of land-based navigation stations participating in the coordinate positioning calculation (in this embodiment, n=4). , Let be the longitude and latitude coordinates of the i-th land-based navigation station.

[0044] 2) Establish a regionally independent coordinate system: On the WGS84 reference ellipsoid, using the latitude and longitude coordinates of the projection center. The projection plane is determined by the point of tangency; on the projection plane, the origin O is the projection center. The X-axis passes through point O and points north along the meridian, the Z-axis passes through point O and is perpendicular to the projection plane, pointing outwards from the reference ellipsoid. The Y-axis, X-axis, and Z-axis form a left-handed rectangular coordinate system, which is the regionally independent coordinate system (e.g., ...). Figure 1 (as shown) 3) Calculate the projected coordinates of the land-based navigation station in the regional independent coordinate system. The calculation formula is as follows: (2) in, Let be the latitude, longitude, and elevation of the i-th land-based navigation station. Let be the projected coordinates of the i-th land-based navigation station in the regional coordinate system, and let e be the first eccentricity of the reference ellipsoid, calculated as follows: (3) Where a and b are the lengths of the major and minor axes of the reference ellipsoid, respectively.

[0045] S2: Construct an algorithm to calculate the starting coordinates of the positioning point, obtain the measurement data and magnetic difference of each navigation station, and calculate the starting coordinates of the positioning point.

[0046] Specifically, the magnetic azimuth and slant range measurements of the aircraft at the positioning point are obtained from each land-based navigation station. Based on the magnetic difference at the location of the navigation station, the starting coordinates of the positioning point in the regional independent coordinate system are calculated using the starting coordinate calculation algorithm (see Table 1 for relevant measurement data in this embodiment).

[0047] The relevant calculation formulas for the algorithm to calculate the starting coordinates of the positioning point are as follows: (4) in, Let be the starting coordinates of the positioning point in the regional independent coordinate system, and n be the number of land-based navigation stations participating in the coordinate positioning calculation. Let be the spatial coordinates of the i-th land-based navigation station in the regional independent coordinate system. Let be the true azimuth of the aircraft based on the i-th navigation station, and , Let be the measured magnetic azimuth angle of the aircraft at the positioning point by the i-th navigation station. Let be the magnetic difference at the location of the i-th navigation station. Let be the slant distance measurement value of the i-th navigation station to the positioning point.

[0048] S3: Based on the starting coordinates of the positioning point and the relevant measurement values ​​of the navigation station, construct a matrix-form expression for the measurement value residual vector.

[0049] Specifically, the residual vector expression of the measurement values ​​is constructed based on the starting coordinates of the positioning point in the regional independent coordinate system and the relevant measurement values ​​of the navigation station. The specific steps are as follows: 1) List the general form of the expression for the residual of the measured value: (5) in, , These are the residuals of the horizontal azimuth and slant range measurements from the land-based navigation station, respectively. For the coordinate components of the positioning point, Let be the spatial coordinates of the i-th land-based navigation station in the regional independent coordinate system; 2) Linearize the general form of the expression for the residuals of the measured values: Based on the general form of the measurement residual expression using the Maclaurin series expansion, retaining the first two terms of the expansion, we obtain the linearized expression for the measurement residual as follows: (6) in, The approximate slant distance between the positioning point and navigation station i is calculated based on the starting coordinates of the positioning point: (7) 3) Based on the above linearized expression for the measured residuals, construct a matrix-form expression for the residual vector: (8) in, The residual vector of measured values: A is the coefficient matrix; Correction vector for coordinate values: c is a vector of constant terms.

[0050] S4: Based on the accuracy characteristics of the navigation station's horizontal azimuth and slant range measurements, calculate and construct the measurement value weight matrix.

[0051] Specifically, the measurement value weight matrix is ​​constructed based on the measurement accuracy characteristics of the navigation station (VOR / DME). The specific steps are as follows: 1) Calculate the weights of the horizontal azimuth and slant range measurements for each navigation station. The calculation formula is as follows: (9) in, , These are the weights of the horizontal azimuth and slant range measurements of the i-th navigation station, respectively. denoted as slant distance measurement of the i-th navigation station; n represents the number of navigation stations involved in solving the coordinates of the positioning point; NM is the unit: nautical mile.

[0052] 2) Construct a measurement value weight matrix based on the weights of the horizontal azimuth and slant range measurements of each navigation station: (10) Where P is the measurement weight matrix.

[0053] S5: Based on the principle of minimizing the weighted sum of squares of the residuals of the measured values, a calculation model for the correction of the coordinate components of the positioning point is established, and the correction and estimated coordinates of the positioning point are calculated.

[0054] Specifically, the positioning point coordinate component correction vector is calculated based on the positioning point coordinate component correction vector calculation model, and then the positioning point coordinate estimate is obtained; 1) Calculate the coordinate component correction vector, using the following formula: (11) in, Correction vector for the coordinate values ​​of the positioning point: , c and c are the transpose of the coefficient matrix and the constant term vector, respectively, in the matrix form of the residual vector expression (Equation (8)); P is the measurement weight matrix.

[0055] 2) Calculate the estimated coordinates of the location point. The calculation formula is as follows: (12) Where (x, y, z) are the estimated coordinates of the positioning point.

[0056] S6: The optimal estimated coordinates of the positioning point are obtained by using an iterative calculation method; Specifically: 1) The j-th iteration calculation results of the coordinate component corrections and coordinate estimates of the positioning point obtained from steps S3 to S5: , j = 0, 1, 2, ...; 2) Set the iterative convergence condition: (13) In this embodiment, Take 0.05 NM.

[0057] 3) Iterative calculations yield the optimal estimated coordinates of the positioning point: The coordinate estimates from this calculation will be used as the starting coordinates for the new positioning point: , , This process is then incorporated into steps S3 through S6 for iterative calculation until the coordinate value correction satisfies the convergence condition. Assuming the convergence condition is met after m iterations, the resulting coordinate estimate is... This is the optimal estimate of the location point coordinates: .

[0058] In this embodiment, the optimal estimated coordinates of each positioning point and the corresponding calculation results of other existing positioning algorithms are detailed in Table 2.

[0059] S7: Construct an algorithm for inverse calculation of oblique axis equidistant tangent azimuth projection coordinates, and convert the optimal estimated coordinates of the positioning point into latitude, longitude and elevation coordinates in the geodetic coordinate system.

[0060] Specifically, the optimal estimate of the coordinates of the positioning point in the region-independent coordinate system is obtained by using the oblique axis equidistant tangent azimuth projection coordinate inverse calculation algorithm: The steps to convert latitude and longitude coordinates and elevation to the WGS84 coordinate system are as follows: 1) Based on the optimal estimate of the positioning point coordinates, calculate the approximate latitude of the positioning point in the WGS84 coordinate system. The calculation formula is as follows: (14) in, These are approximate latitude coordinates of the location point. The latitude of the projection center a The length of the semi-major axis of the reference ellipsoid in the WGS84 coordinate system. e For the first eccentricity, This is the optimal estimate of the ordinate of the positioning point.

[0061] 2) Calculate the deviation of the ordinate in the independent coordinate system of the region based on the approximate latitude coordinates of the positioning point: (15) in, For the first k The approximate latitude value obtained from the next iteration. k=0,1,2,…… ; This refers to the deviation of the ordinate in a regionally independent coordinate system, i.e., based on the latitude approximation. The difference between the calculated ordinate in the regional independent coordinate system and the optimal estimate of the ordinate.

[0062] 3) Calculate the latitude coordinate correction value in the geodetic coordinate system based on the vertical coordinate deviation: (16) in, This is a latitude correction value.

[0063] 4) Correct the latitude coordinates As a new approximation of latitudinal coordinates, it is incorporated into steps 2) through 4) for iterative calculation until the iterative convergence condition is met: (17) in, The deviation of the ordinate in the region-independent coordinate system calculated in step 2) In this embodiment, the ordinate deviation convergence threshold is used. ; At this point, the calculated result That is, the optimal estimate of the coordinates of the positioning point is the latitude in the geodetic coordinate system. .

[0064] 5) Calculate the optimal estimated coordinates of the positioning point using the longitude and elevation in the geodetic coordinate system. The calculation formula is as follows: (18) in, , , These represent the optimal estimated coordinates of the positioning point in the geodetic coordinate system, specifically the latitude, longitude, and elevation. , These are the optimal estimates for the x-coordinate and y-coordinate of the positioning point, respectively. The longitude of the projection center. a The length of the semi-major axis of the reference ellipsoid in the geodetic coordinate system. e First eccentricity In this embodiment, the optimal estimated coordinates of each positioning point in the WGS84 geodetic coordinate system, including latitude and longitude coordinates and elevation, are detailed in Table 2 using the oblique axis equidistant tangent azimuth projection coordinate inverse calculation algorithm.

[0065] S8: Based on the RNP operating rules, construct a positioning accuracy assessment algorithm to calculate the lateral positioning deviation of the aircraft within the 95% confidence interval.

[0066] Implementing RNP operations requires real-time monitoring and alarm capabilities for navigation and positioning performance. The core data support for this capability is the aircraft's lateral positioning deviation within a 95% confidence interval, calculated as follows: 1) Calculate the unit weighted variance Concordance Matrix The calculation formula is as follows: (19) (20) Where n is the number of VOR / DME navigation stations participating in the positioning calculation; the calculated covariance matrix Its composition is as follows: (twenty one) in, , , The variance of the corresponding coordinate components. , , This represents the covariance between the corresponding coordinate components.

[0067] 2) Calculate the parameters of the ellipse for the accuracy distribution of the positioning points. like Figure 4 As shown, the accuracy distribution ellipse parameters include: the positional error along the semi-major axis of the ellipse. σ a Positional error along the minor semi-axis of the ellipse σ b and the true azimuth of the semi-major axis The calculation formula is as follows: (twenty two) Among them, when hour, or ;when hour, .

[0068] 3) Calculate the lateral positioning deviation within the 95% confidence interval. In this embodiment, the true azimuth angle of the aircraft's guiding track is: =213° (e.g.) Figure 5(As shown), lateral positional error The calculation formula is as follows: (twenty three) Since the positional deviation of the positioning point coordinates along any orientation follows a normal distribution, within the 95% confidence interval, the lateral deviation of the aircraft... The calculation formula is: (twenty four) In this embodiment, the calculation results of the lateral positioning deviation of the aircraft at the three positioning points within the 95% confidence interval are detailed in Table 3.

[0069] Based on a flight simulation platform, the calculation results and accuracy comparisons of various positioning point coordinate solving algorithms under land-based navigation are shown in Tables 2 and 3. Compared with existing traditional solving algorithms, the calculation method proposed in this invention significantly reduces the accuracy of coordinate component positioning deviation, planar positioning deviation, and lateral positioning deviation of the guided track, all based on the aircraft's actual position information provided by the flight simulation platform. Specifically, the positioning point coordinate calculation results of this method control the lateral positioning deviation (both theoretical and calculated values ​​within the 95% confidence interval) within 300m (0.16 NM), a core accuracy indicator affecting flight safety, thus meeting the high-precision track guidance requirements of RNP operation.

[0070] Furthermore, VOR / DME single-station positioning and existing multi-station traditional positioning algorithms cannot calculate the lateral positioning deviation within the 95% confidence interval of the positioning point, while this algorithm realizes the calculation of this key accuracy index that is adapted to RNP operation.

[0071] Based on existing ground-based navigation station (VOR / DME) raw measurement data, this embodiment uses aircraft three-dimensional coordinate positioning and accuracy assessment methods to further improve the aircraft's ground-based navigation positioning accuracy and reduce positioning deviation on the basis of existing technology. It also solves the problem that existing ground-based navigation positioning algorithms cannot meet the RNP operating rules and requirements. With the support of ground-based navigation equipment, it realizes the calculation of the lateral positioning deviation of the aircraft within the 95% confidence interval required by the RNP operating specifications, thereby improving the safety and reliability of aviation operations.

[0072] Table 1. Simulation verification of navigation station position, projection, and measurement information.

[0073] The proposed high-precision and rigorous three-dimensional coordinate solution algorithm, along with existing related algorithms, was used to solve for the location coordinates of aircraft at the same plane and pressure altitude. The theoretical coordinates (true values) of the aircraft's location obtained from the simulation platform and the results obtained from each solution algorithm are shown in the table below: Table 2 Simulation Verification of Theoretical Coordinates and Calculation Results of Aircraft Positioning Points .

[0074] Note: "Theoretical coordinates of the positioning point" are derived from the aircraft's actual position information from the flight simulation platform. Table 3 Comparison of Aircraft Position Point Coordinate Calculation Results

[0075] Note: "\" indicates that the corresponding algorithm does not have the ability to calculate this accuracy index; since the flight altitude information that ensures aviation safety should come from barometric altimeters and radio altimeters, rather than the measurement results of external navigation facilities, this embodiment does not compare the accuracy of the positioning point altitude calculation results.

[0076] The above are merely preferred embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for three-dimensional coordinate positioning and accuracy evaluation of aircraft under land-based navigation, characterized in that, Includes the following steps: S1: Construct an oblique axis equidistant tangential projection coordinate forward calculation algorithm to convert the latitude and longitude coordinates and elevation of the land-based navigation station based on the geodetic coordinate system into the projected coordinates of the regional independent coordinate system; S2: Construct an algorithm to calculate the starting coordinates of the positioning point, obtain the measurement data and magnetic difference of each navigation station, and calculate the starting coordinates of the positioning point; S3: Based on the starting coordinates of the positioning point and the relevant measurement values ​​of the navigation station, construct a matrix-form expression for the measurement value residual vector; S4: Calculate and construct the measurement value weight matrix based on the accuracy characteristics of the navigation station's horizontal azimuth and slant range measurements; S5: Based on the principle of minimizing the weighted sum of squares of the residuals of the measured values, establish a calculation model for the correction of the coordinate components of the positioning point, and calculate the correction and estimated coordinates of the positioning point. S6: The optimal estimated coordinates of the positioning point are obtained by using an iterative calculation method; S7: Construct an algorithm for back-calculation of oblique axis equidistant tangential projection coordinates, and convert the optimal estimated coordinates of the positioning point into latitude and longitude coordinates and elevation in the geodetic coordinate system; S8: Based on the RNP operating rules, construct a positioning accuracy assessment algorithm to calculate the lateral positioning deviation of the aircraft within the 95% confidence interval.

2. The method for three-dimensional coordinate positioning and accuracy evaluation of aircraft under land-based navigation as described in claim 1, characterized in that, Construct an algorithm for forward calculation of oblique axis equidistant tangent projection coordinates, including: A method for calculating the latitude and longitude coordinates of the projection center is established to determine the latitude and longitude coordinates of the projection center in the geodetic coordinate system; On the reference ellipsoid corresponding to the geodetic coordinate system, construct a tangent plane with the projection center as the tangent point, and use this tangent plane as the projection plane; On the projection plane, with the projection center as the origin O, the X-axis passes through point O and points north of the meridian, the Z-axis passes through point O and is perpendicular to the projection plane, pointing outward from the reference ellipsoid, and the Y-axis, together with the X-axis and Z-axis, forms a left-handed spatial rectangular coordinate system, which is the regional independent coordinate system. On the projection plane, the distance along the meridian or parallel is equal to the actual distance in the corresponding direction on the reference ellipsoid, with no length projection distortion; The latitude, longitude, and elevation coordinates of the land-based navigation station based on the geodetic coordinate system are obtained, and the projected coordinates of the land-based navigation station in the regional independent coordinate system are calculated.

3. The method for three-dimensional coordinate positioning and accuracy evaluation of aircraft under land-based navigation as described in claim 2, characterized in that, A method for calculating the latitude and longitude coordinates of the projection center is constructed, including: Determine the number of land-based navigation stations participating in the coordinate positioning calculation, and obtain the latitude and longitude coordinates of each land-based navigation station based on the geodetic coordinate system; Calculate the arithmetic mean of the minimum and maximum longitude coordinates of each land-based navigation station, and use it as the longitude coordinate of the projection center; Calculate the arithmetic mean of the minimum and maximum latitude coordinates of each land-based navigation station to obtain the latitude coordinates of the projection center.

4. The method for three-dimensional coordinate positioning and accuracy evaluation of aircraft under land-based navigation as described in claim 3, characterized in that, The projected coordinates of the land-based navigation station in the regional independent coordinate system are calculated, including: Based on the lengths of the semi-major and semi-minor axes of the reference ellipsoid, the first eccentricity of the reference ellipsoid is calculated. Obtain the latitude, longitude, and elevation coordinates of each land-based navigation station in the geodetic coordinate system; The latitude and longitude coordinates of the projection center are obtained using the method of calculating the latitude and longitude coordinates of the projection center in the independent coordinate system of the area where the navigation station is located; Based on the latitude and longitude coordinates of the projection center and the latitude, longitude, and elevation of the land-based navigation station, the projected coordinates of the land-based navigation station in the regional independent coordinate system are calculated.

5. The method for three-dimensional coordinate positioning and accuracy evaluation of aircraft under land-based navigation as described in claim 4, characterized in that, An algorithm for calculating the starting coordinates of a location point is constructed, including: The magnetic azimuth and slant distance measurements of each land-based navigation station and the local magnetic difference are obtained, and the starting coordinates of the positioning point in the regional independent coordinate system are calculated.

6. The method for three-dimensional coordinate positioning and accuracy evaluation of aircraft under land-based navigation as described in claim 5, characterized in that, Based on the starting coordinates of the positioning point and the relevant measurements from the navigation station, a matrix-form expression for the measurement residual vector is constructed, including: Based on the starting coordinates of the positioning point and the relevant measurement values ​​of the navigation station, the general form of the expression for the measurement residual is listed; Expanding the above expression using the Maclaurin series and retaining the first two terms yields a linearized residual expression. Construct a matrix form of the residual vector expression based on the linearized residual expression.

7. The method for three-dimensional coordinate positioning and accuracy evaluation of aircraft under land-based navigation as described in claim 6, characterized in that, Based on the accuracy characteristics of the navigation station's horizontal azimuth and slant range measurements, a measurement value weight matrix is ​​calculated and constructed, including: Calculate the weights of the horizontal azimuth and slant range measurements for each land-based navigation station; A measurement value weight matrix is ​​constructed based on the weights of the relevant measurement values ​​of each navigation station.

8. The method for three-dimensional coordinate positioning and accuracy evaluation of aircraft under land-based navigation as described in claim 7, characterized in that, The optimal estimated coordinates of the positioning point are obtained by using an iterative calculation method, including: Based on the matrix form of the residual vector expression and the measurement value weight matrix, a calculation model for the correction of the positioning point coordinate components is established, and the correction of the positioning point coordinate components and the estimated positioning point coordinates are calculated. The estimated coordinates of the positioning point are used as the new starting coordinates of the positioning point, and the new starting coordinates of the positioning point are incorporated into steps S3 to S6 for iterative calculation until the coordinate value correction satisfies the convergence condition. The result obtained is the optimal estimated coordinates of the positioning point.

9. The method for three-dimensional coordinate positioning and accuracy evaluation of aircraft under land-based navigation as described in claim 8, characterized in that, An algorithm for inverse calculation of oblique axis equidistant tangent projection coordinates is constructed to convert the optimal estimated coordinates of the positioning point into latitude, longitude, and elevation coordinates in the geodetic coordinate system, including: The approximate latitude of the positioning point is calculated based on the ordinate of the positioning point in the regional independent coordinate system, the latitude of the projection center, and the reference ellipsoid parameters. The deviation of the ordinate in the independent coordinate system of the region is calculated based on the latitude approximation, and then the latitude correction value is obtained. The latitude correction value is used as a new latitude approximation for iterative calculation until the iterative convergence condition is met, and the latitude of the positioning point in the geodetic coordinate system is obtained. The longitude and elevation of the positioning point in the geodetic coordinate system are calculated based on the abscissa and ordinate of the positioning point in the regional independent coordinate system, the longitude of the projection center, and the reference ellipsoid parameters.

10. A method for three-dimensional coordinate positioning and accuracy evaluation of aircraft under land-based navigation as described in claim 9, characterized in that, Calculate the lateral positioning deviation of the aircraft within the 95% confidence interval, including: Calculate the unit weight variance and covariance matrix; Calculate the parameters of the ellipse for the accuracy distribution of the positioning points; Calculate the lateral positioning deviation of the aircraft within the 95% confidence interval.

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