A near-surface trajectory reconstruction method and system based on earth line recursion

Abstract

The application discloses a near-surface trajectory reconstruction method and system based on geodesic line recursion, and belongs to the technical field of navigation equipment testing. i，i+1 The application extracts the projection length (S i，i+1 , s-K i‑1，i，e ) and elevation change information (h i+1 -h i ) of adjacent points in measured positioning data, adopts the principle of keeping the change of the ground heading and the invariable ground height, starts from the initial place (including h0) and initial direction of the simulation area set by human beings, carries out simulation trajectory recursion, and completes the reconstruction of the measured trajectory in any area on the ground. The application is proved by mathematics to meet the same ground movement characteristics of the reconstructed trajectory and the measured trajectory, provides a rigorous theoretical basis for the identification of subsequent evaluation results, and can be applied to the trajectory reconstruction of any place and any direction, and increases the flexibility of the test design.

Description

Technical Field

[0001] This invention belongs to the field of navigation equipment testing technology, and more specifically, relates to a method and system for reconstructing near-surface trajectories based on geodesic recursion. Background Technology

[0002] Before inertial navigation equipment is handed over for application, it needs to undergo accuracy testing to assess whether its performance meets the standards. However, the geographical location of the Earth's poles makes it inconvenient for countries in the low and mid-latitudes, such as China, to conduct field tests. Furthermore, due to the differences in the polar region programming algorithm and working mode between inertial navigation and the low and mid-latitudes, this stage of verification cannot be omitted.

[0003] Therefore, previous researchers have studied virtual polar region technology, which uses mathematical methods to transform experimental data from mid- and low-latitude regions to polar regions for equivalent navigation test verification. The trajectory reconstruction process is one of the key steps in virtual polar region technology, aiming to plan a motion trajectory in the polar region similar to that of the actual experimental test.

[0004] Patent CN2019107309381 discloses a trajectory reconstruction method based on a lateral geographic coordinate system. By adopting the trajectory reconstruction principle of keeping the attitude matrix, velocity and altitude information under the lateral geographic system unchanged, the polar position trajectory is reconstructed by integrating the lateral velocity after compensating the ellipsoid correction coefficient.

[0005] However, this method has the following drawbacks and limitations: it actually alters the motion characteristics of the carrier relative to the local horizontal plane, which contradicts the original design intent and introduces additional errors into the experiment, making subsequent accuracy evaluation more difficult. Furthermore, existing technologies cannot flexibly set the position and direction of the reconstructed trajectory, resulting in significant limitations. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the present invention aims to provide a near-surface trajectory reconstruction method and system based on geodesic recursion, which addresses the problem of how to reconstruct the trajectory while maintaining the carrier's motion relative to the ground.

[0007] To achieve the above objectives, in a first aspect, the present invention provides a near-surface trajectory reconstruction method based on geodesic recursion, wherein the recursion from point i to point i+1 in the simulated region includes:

[0008] Step 1: Calculate the average latitude B for the measured time period [i, i+1] = (B i +B i+1 ) / 2, and then calculate the measured local meridian radius M and the measured local zonal radius N;

[0009] Step 2: Calculate the geodesic azimuth change dK of the flight path during this period and the projected length S of the geodesic between adjacent points. i,i+1 :

[0010] dK=sinB×dL

[0011]

[0012] Step 3: Calculate cosK, and determine the quadrant in which K lies based on the signs of dB and dL, and then deduce the average azimuth angle K:

[0013] cosK = MdB / S i,i+1

[0014] Step 4: Calculate the initial azimuth angle K i,i+1,s Termination azimuth angle K i,i+1,e and the initial azimuth angle of the simulated trajectory during this period

[0015]

[0016]

[0017]

[0018] Step 5: Calculate the projected length of the earth line between adjacent points on the simulated trajectory.

[0019]

[0020] Step 6: Based on the latitude of the simulated position at time i Calculate the radius M of the meridian in the simulated region. * And the radius N of the simulated region's east-west circle * ;

[0021] Step 7: Calculate the latitude increment (dB) of the simulated trajectory during this period. * The longitude increment dL of the simulated trajectory during this period * And the change in geodesic azimuth angle dK of the simulated trajectory during this period * :

[0022]

[0023]

[0024]

[0025] Step 9: Calculate the simulated position of the carrier at time i+1. and the azimuth angle of the simulated trajectory termination

[0026]

[0027]

[0028]

[0029] Wherein, the latitude increment dB = B during this period i+1 -B i The longitude increment during this period is dL = L i+1 -L i R represents the radius of curvature of the Earth's surface where the measured trajectory segment is located; R * This represents the radius of curvature of the Earth's surface where the simulated trajectory segment is located. h represents the longitude of the simulated position at time i. i+1 This represents the altitude of the carrier at time i+1.

[0030] Preferably, the interval between Step 7 and Step 9 includes:

[0031] Step 8: Use Replace the parts in Steps 5 through 7 respectively. and Repeat Steps 5 through 7 until the accuracy requirements are met.

[0032] Preferably, the radius of curvature of the ground surface where the measured trajectory segment is located...

[0033] Preferably, the radius of curvature of the Earth's surface where the simulated trajectory segment is located...

[0034] To achieve the above objectives, in a second aspect, the present invention provides a near-surface trajectory reconstruction system based on geodesic recursion, comprising: a processor and a memory; the memory for storing computer execution instructions; and the processor for executing the computer execution instructions such that the method described in the first aspect is executed.

[0035] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art:

[0036] This invention proposes a near-surface trajectory reconstruction method and system based on geodesic recursion. This method extracts the projected length (S) of the geodesic between adjacent points in the measured positioning data. i,i+1 ), the geodetic angle at each positioning point (K) i,i+1,s -K i-1,i,e ) and elevation change information (h i+1 -h i The simulation area adopts the principle of maintaining the change in heading and the constant altitude, and the initial location of the simulation area is set manually. include h0) and initial direction The process begins with simulated trajectory recursion to reconstruct the measured trajectory in any region of the Earth's surface. This invention has been mathematically proven to ensure that the reconstructed trajectory shares the same ground motion characteristics as the measured trajectory, providing a rigorous theoretical basis for subsequent evaluation. Furthermore, this invention is applicable to trajectory reconstruction at any location and in any direction, increasing the flexibility of experimental design. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of the geodetic element calculation of the measured trajectory provided by the present invention.

[0038] Figure 2 This is a schematic diagram illustrating the calculation of geodetic elements for the simulated trajectory provided by the present invention.

[0039] Figure 3 The flowchart of a near-surface trajectory reconstruction method based on geodesic recursion 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] The conventions for initial conditions and variable symbols in this invention are as follows:

[0042] (1) The Earth is regarded as a rotating ellipsoid, the geoid is approximately regarded as an ellipsoid, and the geodetic height is regarded as the ellipsoidal height;

[0043] (2) Given that the carrier begins its voyage at time 0, its position information is measured. Let P... i The position of the carrier at time i is represented by variable B. i L i h i The components represent the geodetic latitude, geodetic longitude, and geodetic altitude of the carrier at time i. In this invention, the "carrier" refers to any object near the Earth's surface that moves with reference to the ground, such as vehicles, ships, submersibles, and aircraft.

[0044] (3) Set the initial location at the same geodetic height according to the test requirements. By variables h0 is composed of the initial latitude, initial longitude, and initial altitude of the simulation area, respectively. The initial direction of motion is... (North by east is positive, 0-360°).

[0045] (4) In this invention, all quantities without asterisks represent quantities in the experimental process, and all quantities with asterisks represent quantities in the simulation process.

[0046] Figure 1 This is a schematic diagram of the geodetic element calculation of the measured trajectory provided by the present invention. Figure 2 This is a schematic diagram of the geodetic element calculation for the simulated trajectory provided by the present invention. The situation shown in the diagram is the trajectory reconstruction on the ground surface, i.e., the elevation is 0. The trajectory of a carrier with elevation changes is still a geodetic line projected onto the ground surface. The projection distance of a trajectory of the same length onto the ground is different under different ground curvatures, and the geodetic elevation changes linearly.

[0047] like Figure 3 As shown, this invention proposes a near-surface trajectory reconstruction method based on geodesic recursion, h ab =H b -H a The recursive process from point i (corresponding to time i) in the simulated region to point i+1 is as follows:

[0048] Step 1: Calculate the measured local meridian radius M and the measured local trochanter radius N:

[0049]

[0050] Where a represents the length of the semi-major axis of the Earth ellipsoid, e represents the eccentricity of the Earth ellipsoid, and the average latitude during this period is B = (B i +B i+1 ) / 2.

[0051] Step 2: Calculate the geodesic azimuth change dK of the flight path during this period and the projected length S of the geodesic between adjacent points. i,i+1 :

[0052] dK=sinB×dL

[0053]

[0054] Wherein, the latitude increment dB = B during this period i+1 -B i The longitude increment during this period is dL = L i+1 -L i .

[0055] Step 3: Calculate cosK, and determine the quadrant in which K lies based on the signs of dB and dL, thereby determining the specific value of the average azimuth angle K:

[0056] cosK = MdB / S i,i+1

[0057] If dB is the y-axis and dL is the x-axis, then if dB>0 and dL>0, K is in the first quadrant; if dB>0 and dL<0, it is in the second quadrant, and so on.

[0058] Step 4: Calculate the initial azimuth angle Ki,i+1,s Termination azimuth angle K i,i+1,e and the initial azimuth angle of the simulated trajectory during this period (This term is only calculated when i≠0):

[0059]

[0060]

[0061]

[0062] Step 5: Calculate the projected length of the earth line between adjacent points on the simulated trajectory.

[0063]

[0064] Among them, the radius of curvature of the ground surface where the measured trajectory segment is located The radius of curvature of the ground surface where the simulated trajectory segment is located This represents the latitude of the simulated position at time i.

[0065] Step 6: Calculate the radius M of the meridian circle in the simulated region. * And the radius N of the simulated region's east-west circle * :

[0066]

[0067] Step 7: Calculate the latitude increment (dB) of the simulated trajectory during this period. * The longitude increment dL of the simulated trajectory during this period * And the change in geodesic azimuth angle dK of the simulated trajectory during this period * :

[0068]

[0069]

[0070]

[0071] Step 8: To improve calculation accuracy, you can use... Replace Steps 5 through 7 and Repeat Steps 5 through 7. The iteration can stop when a threshold is reached or the required precision is achieved.

[0072] Step 9: Calculate the simulated position of the carrier at time i+1. and the azimuth angle of the simulated trajectory termination

[0073]

[0074]

[0075]

[0076] in, This represents the longitude of the simulated position at time i.

[0077] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for reconstructing near-surface trajectories based on geodesic recursion, characterized in that, The recursion from point i to point i+1 in the simulated region includes: Step 1: Calculate the average latitude B for the measured time period [i, i+1] = (B i +B i+1 ) / 2, and then calculate the measured local meridian radius M and the measured local zonal radius N; Step 2: Calculate the geoid azimuth change dK of the measured flight track during this period and the projected length S of the geoid between adjacent points. i,i+1 : dK=sinB×dL Step 3: Calculate cosK, and determine the quadrant in which K lies based on the signs of dB and dK, and then deduce the mean azimuth angle K: cosK=MdB / S i，i+1 Step 4: Calculate the initial azimuth angle K i，i+1，s Termination azimuth angle K i，i+1，e and the initial azimuth angle of the simulated trajectory during that time period Step 5: Calculate the projected length of the earth line between adjacent points on the simulated trajectory. Step 6: Based on the latitude of the simulated position at time i Calculate the radius M of the meridian in the simulated region. * And the radius N of the simulated region's east-west circle * ; Step 7: Calculate the latitude increment (dB) of the simulated trajectory during this period. * The longitude increment dK of the simulated trajectory during this period * And the change in geodesic azimuth angle dK of the simulated trajectory during this period * : Step 9: Calculate the simulated position of the carrier at time i+1. and the azimuth angle of the simulated trajectory termination Wherein, the latitude increment dB = B during this period i+1 -B i The longitude increment during this period is dL = L i+1 -L i R represents the radius of curvature of the Earth's surface where the measured trajectory segment is located; R * This represents the radius of curvature of the Earth's surface where the simulated trajectory segment is located. h represents the longitude of the simulated position at time i. i+1 This represents the altitude of the carrier at time i+1.

2. The method as described in claim 1, characterized in that, The period between Step 7 and Step 9 includes: Step 8: Use Replace the parts in Steps 5 through 7 respectively. and Repeat Steps 5 through 7 until the accuracy requirements are met.

3. The method as described in claim 1 or 2, characterized in that, Radius of curvature of the ground surface where the measured trajectory segment is located 4. The method as described in claim 1 or 2, characterized in that, The radius of curvature of the ground surface where the simulated trajectory segment is located 5. A near-surface trajectory reconstruction system based on geodesic recursion, 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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