A virtual polar region initialization method and system based on a variable transverse coordinate system

Abstract

The application discloses a virtual polar region initialization method and system based on a variable transverse coordinate system and belongs to the technical field of navigation equipment testing. The application fully utilizes the variability of the transverse coordinate system definition, namely the fact that the transverse earth coordinate system can rotate by an arbitrary angle around the earth polar axis, projects the measured trajectory and the virtual trajectory into different defined transverse geographical coordinate systems, calculates the definition of the transverse coordinate system according to the initial place and the initial azimuth angle of the virtual polar region, realizes the transfer from the measured trajectory to the global arbitrary place and the arbitrary direction, greatly reduces the trajectory deformation, and thus meets the demand of the simulation voyage diversification setting in the inertial navigation polar region simulation test.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of navigation equipment testing, and more particularly relates to a virtual polar region initialization method and system based on a variable transverse coordinate system. BACKGROUND

[0002] In the virtual polar region technology for inertial navigation system testing, the "Virtual Polar Region Method Based on the Earth's Transverse Ellipsoid Model" provides a trajectory transplantation method based on transverse speed and attitude invariance, which adopts transverse speed recursion of transverse latitude and longitude information, and can better realize the transplantation of mid-low latitude trajectories to the polar region. When this method is used for polar inertial navigation IMU data simulation generation, it has the advantages of determined expression formula form and convenient error analysis, and therefore is applied in the virtual polar region technology.

[0003] Patent CN2019107309381 discloses a virtual polar region initialization method, which starts from an artificially set simulation initial location, and reconstructs the polar region position trajectory by integrating the transverse speed after compensating the ellipsoid correction coefficient.

[0004] However, this method has the following defects and deficiencies: a transverse coordinate system is used for all links, i.e., a standard transverse coordinate system with the 0° meridian and the 180° meridian as the transverse equator and the 90°E and the intersection of the equator as the transverse north pole, which causes great trajectory deformation after the reconstruction of low-latitude trajectories close to the transverse earth coordinate system polar point. In addition, due to the adoption of the trajectory reconstruction principle of keeping the transverse speed unchanged, the initial direction of the reconstructed trajectory is determined and cannot be flexibly adjusted, which is not conducive to the development of multi-sample tests. SUMMARY

[0005] In view of the defects of the prior art, the present application aims to provide a virtual polar region initialization method and system based on a variable transverse coordinate system, which aims to solve the problem that the existing method depends on real measurement data for the selection of the initial location and the initial azimuth angle in trajectory simulation, and the large deformation degree of the trajectory.

[0006] To achieve the above-mentioned purpose, in a first aspect, the present application provides a virtual polar region initialization method based on a variable transverse coordinate system, which comprises:

[0007] Step 0: obtaining the initial azimuth angle of the virtual region artificially set or the position of the initial two points of the measured trajectory the geographical latitude of the virtual region starting location B m0 and the geographical longitude of the virtual region starting location Lm0 North by East is positive;

[0008] Step 1: Calculate the horizontal coordinate of the starting point of the measured trajectory

[0009]

[0010] Wherein, B0 represents the geographic latitude of the starting point of the measured trajectory, L0 represents the geographic longitude of the starting point of the measured trajectory; represents the horizontal latitude of the starting point of the measured trajectory, λ t (0) represents the horizontal longitude of the starting point of the measured trajectory;

[0011] Step 2: According to the obtained starting point position and initial azimuth angle of the measured trajectory or the position of the initial two points of the measured trajectory, calculate the initial horizontal azimuth angle ψ t (0);

[0012] Step 3: Determine the horizontal-geographic rotation angle of the virtual polar region Calculate the intermediate variable L x :

[0013]

[0014] Step 4: Determine the child horizontal system suitable for the virtual polar region by the horizontal equator of the eastern hemisphere passing through the geographic longitude L m0 -L x

[0015] Preferably, Step 2 is as follows:

[0016] After obtaining the geographic position (B1, L1) of the next point of the starting point of the measured trajectory, first calculate the horizontal coordinate of the second point of the measured trajectory

[0017]

[0018] Wherein, B1 represents the geographic latitude of the next point of the starting point of the measured trajectory, L1 represents the geographic longitude of the next point of the starting point of the measured trajectory; represents the horizontal latitude of the next point of the starting point of the measured trajectory, λ t (1) represents the horizontal longitude of the next point of the starting point of the measured trajectory;

[0019] Calculate the horizontal latitude change and horizontal longitude change between the initial two points:

[0020]

[0021] Determine the parameters of the conversion matrix:

[0022] ​

[0023] wherein e represents the eccentricity of the earth ellipsoid, and the time interval is the time interval between the two points the time interval is the time interval between the two points t = (λ t (0) + λ t (1)) / 2

[0024] the initial transverse velocity V tE (0) and V tN (0) are calculated again

[0025]

[0026] wherein V tE (0) represents the initial transverse eastward velocity, V tN (0) represents the initial transverse northward velocity, and dt represents the time interval between the two points

[0027] the initial transverse azimuth angle ψ t (0) is calculated

[0028] ψ t (0) = arctan2 (V tN (0), V tE (0))

[0029] wherein arctan2 (x, y) represents the tangent value of the angle between the line connecting the origin O and the straight coordinate point (x, y) of the plane and the OX axis in the counterclockwise direction.

[0030] Preferably, the calculation formula of the prime vertical radius N is as follows:

[0031]

[0032] wherein a represents the length of the semi-major axis of the earth ellipsoid.

[0033] Preferably, Step 2 is specifically as follows: when the initial azimuth angle K0 of the measured trajectory is obtained, the initial transverse azimuth angle ψ t (0) is directly calculated

[0034]

[0035] To achieve the above object, in a second aspect, the application provides a virtual polar region initialization system based on a variable transverse coordinate system, comprising: a processor and a memory; the memory is used for storing computer execution instructions; the processor is used for executing the computer execution instructions, so that the method as described in the first aspect is executed.

[0036] Overall, compared with the prior art, the above technical scheme conceived by the application has the following beneficial effects:

[0037] This invention discloses a virtual polar region initialization method and system based on a variable transverse coordinate system. It fully utilizes the variability of the transverse coordinate system definition, namely, the fact that the transverse Earth coordinate system can rotate around the Earth's polar axis by any angle. The measured trajectory and the virtual trajectory are projected onto transverse geographic coordinate systems with different definitions. The definition of the transverse coordinate system used is calculated based on the initial location and initial azimuth of the virtual polar region. It can realize the transfer from the measured trajectory to any location and any direction in the world, while greatly reducing the trajectory deformation, thereby meeting the needs of diverse settings for simulated voyages in inertial navigation polar region simulation tests. Attached Figure Description

[0038] Figure 1 This is a schematic diagram of the ellipsoidal transverse coordinate system provided by the present invention.

[0039] Figure 2 The flowchart of a virtual polar region initialization method based on a variable transverse coordinate system provided by the present invention is shown. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0041] like Figure 1 As shown, the transverse Earth coordinate system is obtained by flipping the traditional Earth coordinate system by 90°. It was initially used to construct the transverse inertial navigation system to solve the polar navigation problem, in order to eliminate the singularity of the traditional inertial navigation system near the poles.

[0042] By comparing the horizontal coordinate system with the traditional coordinate system, we can see that: two symmetrical points on the equator become the horizontal North and South Poles; the original pole (the intersection of the z-axis and the Earth's ellipsoid) lies on the horizontal equator; the horizontal prime meridian passes through the geographic North Pole; and horizontal latitude and longitude... The lateral coordinate system is still defined by the angle between the ellipsoidal surface normal and the relevant plane. However, the ellipsoid is asymmetrical about the lateral polar axis, causing the lateral latitude circles to become irregular spatial curves. In the construction of the lateral geographic coordinate system, the lateral east direction is defined by the tangent direction of the lateral auxiliary latitude circle, and the lateral north direction is determined according to the right-hand rule. This also makes the updating of lateral position more complex, as changes in lateral latitude and longitude are simultaneously affected by the lateral east and lateral north velocities. This invention stipulates that: a superscript of 't' corresponds to lateral latitude and longitude, while a superscript without 't' corresponds to geographic latitude and longitude; a superscript with an asterisk (*) corresponds to the simulated trajectory, while a superscript without an asterisk (*) corresponds to the actual trajectory.

[0043] The lateral position update equation is as follows:

[0044]

[0045] wherein, respectively represent the transverse latitude rate of change, the transverse longitude rate of change, V tE , V tN respectively represent the transverse eastward velocity and the transverse northward velocity, e represents the earth ellipsoid eccentricity, and N represents the local prime vertical radius. This is the position updating formula in the transverse arrangement of inertial navigation.

[0046] If the transverse velocity v t at each time of the measured trajectory is extracted, and the above updating equation is used to calculate from the initial position in the simulation area, a trajectory can be obtained. This is the trajectory transplantation algorithm based on the invariance of the transverse velocity in the background technology (in the present application, the attitude is not considered).

[0047] The conversion relationship between geographical longitude and latitude and transverse longitude and latitude is as follows:

[0048]

[0049] (1) General transverse coordinate system idea:

[0050] The transverse prime meridian is constant through the geographical north pole, and when the transverse earth coordinate system is rotated around the x t axis, a new transverse earth coordinate system and a corresponding transverse geographical coordinate system can be formed. All transverse coordinate systems contained therein are referred to as a transverse coordinate system family, simply referred to as a “transverse system family”, and each transverse coordinate system is referred to as a “sub-transverse system”. Among them, the coordinate system defined by 90°E and the intersection point of the equator as the transverse north pole is the standard transverse coordinate system, also known as the Donald coordinate system. Unless otherwise specified, all equations related to the relationship between the transverse position and the traditional geographical position are only applicable to the standard transverse coordinate system, but only need to convert the geographical longitude to be applicable to other sub-transverse systems.

[0051] (2) Technical concept of the present application:

[0052] Because the poles of different sub-transverse earth systems in the transverse system family are located at different positions on the original equator, it provides convenience for the application of the algorithm. Generally, the measured initial position can be set on the transverse equator to obtain a measured applicable sub-transverse coordinate system; and the definition of the transverse coordinate system is adjusted to construct a simulation calculation applicable sub-transverse coordinate system, and the principle is to make the simulation initial transverse azimuth angle the same as the measured initial transverse azimuth angle.

[0053] As shown in the Figure 2 , the present application discloses a virtual polar region initialization method based on a variable transverse coordinate system, comprising:

[0054] Given conditions: the geographic latitude B0 and geographic longitude L0 of the starting point of the measured trajectory, the geographic latitude B1 and geographic longitude L1 of the next point on the measured trajectory, or the initial azimuth K0 of the measured trajectory (north-east is positive), and the initial azimuth manually set in the virtual area. (North by east is positive), virtual region starting location geographical latitude B m0 The starting location of the virtual region is the geographical longitude L. m0 .

[0055] Requested: Definitions of sub-lateral Earth systems applicable to measured regions and sub-lateral Earth systems applicable to virtual polar regions.

[0056] To avoid excessive classification and discussion, let's take the migration from the mid-to-low latitudes of the Northern Hemisphere to the Arctic region as an example.

[0057] Step 1: The sub-lateral Earth system applicable to the measured area is defined as the lateral Earth system that passes through the L0 meridian of the equator in the Eastern Hemisphere. Calculate the x-coordinate of the starting point of the measured trajectory.

[0058]

[0059] Step 2: Calculate the initial azimuth angle.

[0060] Case a (Given the geographical location (B1, L1) of the next point on the measured trajectory):

[0061] Calculate the x-coordinate of the second point on the measured trajectory.

[0062]

[0063] remember

[0064]

[0065] remember

[0066]

[0067] Where e represents the Earth's ellipsoidal eccentricity, and the average latitude of the first time period. Average longitude λ in the first period t =(λ t (0)+λ t (1)) / 2.

[0068] Find the initial lateral velocity V tE (0), V tN (0):

[0069]

[0070] where dt represents the time interval between two points, and N represents the radius of the prime vertical circle.

[0071]

[0072] where a represents the length of the semi-major axis of the earth ellipsoid.

[0073] The initial transverse azimuth (positive for transverse north and east) is calculated as:

[0074] ψ t (0) = arctan2 (V tN (0), V tE (0))

[0075] "arctan2(x,y)" represents the tangent value of the anticlockwise angle between the line connecting the origin O and the rectangular coordinate point (x,y) of the plane and the OX axis.

[0076] Case b (known initial azimuth K0 of the measured track):

[0077]

[0078] Step 3: Record the virtual polar region transverse - geographic rotation angle Calculate the intermediate variable L x :

[0079]

[0080] When σ = 0,

[0081] L x = 0

[0082] When σ = π,

[0083] L x = π

[0084] Step 4: Determine the appropriate sub-transverse system for the virtual polar region.

[0085] The transverse coordinate system suitable for simulation solution is defined by the transverse east half-sphere equator passing through the geographic meridian L m0 -L x .

[0086] Embodiment

[0087] For a certain actual voyage, the starting point of the route (B0, L0) is (18°26'55"N, 111°06'49"E), and the initial azimuth K0 is 85.0127°. The initial position (B m0 , Lm0 ) set to (79°N, 150°E), initial azimuth set to 299°, calculate definitions of two sub-transverse systems applicable to the measured trajectory and the virtual polar region:

[0088] Sub-transverse system applicable to the measured trajectory, defined by the transverse East-Hemisphere equator passing through 111.3611°E. Calculate in turn the initial transverse azimuth ψ t (0) = -4.9873°, σ = 303.9873°, L x = -145.5186°.

[0089] L m0 - L x = 150° - (-145.5186°) = 295.5186°, i.e. -64.4814°.

[0090] Obtain the transverse coordinate system applicable to the simulated solution, defined by the transverse East-Hemisphere equator passing through 64.4814°W.

[0091] It is to be understood that the above-described embodiments are merely exemplary of the application and that various modifications, equivalent substitutions and changes commensurate with the spirit and principles of the application can be made by those skilled in the art without departing from the invention.

Claims

1. A method for initializing virtual polar regions based on a variable transverse coordinate system, characterized in that, The method includes: Step 0: Obtain the starting position and initial azimuth of the measured trajectory, or the positions of the initial two points of the measured trajectory, and obtain the initial azimuth manually set in the virtual area. Virtual region starting location geographical latitude B m0 And the starting location of the virtual region, geographical longitude L m0 North-southeast is considered positive. Step 1: Calculate the x-coordinate of the starting point of the measured trajectory. Where B0 represents the geographical latitude of the starting point of the measured trajectory, and L0 represents the geographical longitude of the starting point of the measured trajectory; λ represents the lateral latitude of the starting point of the measured trajectory. t (0) indicates the lateral longitude of the starting point of the measured trajectory; Step 2: Calculate the initial horizontal azimuth angle ψ based on the obtained starting position and initial azimuth angle of the measured trajectory, or the positions of the two initial points of the measured trajectory. t (0); Step 3: Determine the lateral-geographical rotation angle of the virtual polar region Then calculate the intermediate variable L x : Step 4: Cross the geographical meridian L from the equator of the Eastern Hemisphere. m0 -L x Determine the sub-lateral system applicable to the virtual polar region.

2. The method as described in claim 1, characterized in that, Step 2 is as follows: After obtaining the geographical location (B1, L1) of the next point after the starting point of the measured trajectory, first calculate the x-coordinate of the second point on the measured trajectory. Where B1 represents the geographical latitude of the point below the starting point of the measured trajectory, and L1 represents the geographical longitude of the point below the starting point of the measured trajectory. λ represents the lateral latitude of the point below the starting point of the measured trajectory. t (1) Represents the lateral longitude of the point below the starting point of the measured trajectory; Calculate the lateral latitude and lateral longitude changes between the initial two points over a given time interval: Determine the parameters of the transformation matrix: Where e represents the Earth's ellipsoidal eccentricity, and the average lateral latitude during this period. The average transverse longitude λ during this period t =(λ t (0)+λ t (1)) / 2; Next, calculate the initial lateral velocity V. tE (0), V tN (0): Among them, V tE (0) represents the initial transverse eastward velocity, V tN (0) represents the initial transverse north velocity, dt represents the time interval between the two points, and N represents the radius of the zonal circle; Then calculate the initial transverse azimuth angle ψ. t (0): ψ t (0)=arctan2(V tN (0),V tE (0)) Here, arctan2(x,y) represents the tangent of the angle between the line connecting the origin and the Cartesian coordinate point (x,y) and the OX axis in a counterclockwise direction.

3. The method as described in claim 2, characterized in that, The formula for calculating the radius N of the zonal circle is as follows: Where 'a' represents the length of the semi-major axis of the Earth's ellipsoid.

4. The method as described in claim 1, characterized in that, Step 2 is as follows: When the initial azimuth angle K0 of the measured trajectory is obtained, the initial transverse azimuth angle ψ is directly calculated. t (0):

5. A virtual polar region initialization system based on a variable transverse coordinate system, characterized in that, include: Processor and memory; The memory is used to store computer-executed instructions; The processor is configured to execute the computer execution instructions, such that the method described in any one of claims 1 to 4 is executed.

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