Method for calculating a drift based on a great circle projection

Abstract

The application discloses a yaw distance calculation method based on a great circle projection, which takes the starting point longitude and latitude, the ending point longitude and latitude of a predetermined flight section and real-time longitude and latitude of an airplane as inputs, regards the earth as a regular sphere, and uses a solid geometry method to deduce accurate yaw distance data, and the error of the calculation result only comes from the difference between the earth and the imaginary regular sphere. The application is simple to calculate, has little influence on system performance, and is suitable for popularization and use in embedded real-time systems or simulation systems.

Description

Technical Field

[0001] This invention relates to a method for calculating yaw distance in an aircraft navigation system, and particularly to a method for calculating yaw distance based on great circle projection. This calculation method can be embedded as an independent and reusable software module in the navigation system or display system software. Background Technology

[0002] Yaw distance refers to the vertical distance between the aircraft's actual position and the planned flight path. It is a crucial navigation data point on the aircraft's cockpit display system, and the accuracy of yaw distance calculation directly impacts the accuracy of aircraft flight. In practical engineering, due to the limited computing resources of airborne embedded devices, approximate calculation methods are often used to calculate yaw distance data in order to reduce resource utilization and avoid affecting the real-time performance of the software. For example, the three points on the flight segment—from point A, to point B, and the aircraft's position—are used as the three vertices of a triangle, and the vertical distance from the aircraft point to the flight path is directly calculated. Obviously, this method has a certain degree of error. Researching a method that can calculate yaw distance more accurately without increasing computational complexity is of practical significance for improving aircraft navigation accuracy. Summary of the Invention

[0003] The purpose of this invention is to provide a method for calculating yaw distance based on great circle projection. It assumes the Earth is a perfect sphere with a radius of 6371 kilometers. Using the starting and ending latitude and longitude of the predetermined flight segment, as well as the aircraft's real-time latitude and longitude, as inputs, accurate yaw distance data is derived using solid geometry methods. The error in the calculation result stems solely from the difference between the Earth and the hypothetical perfect sphere. Clearly, this calculation method is more accurate than the aforementioned approximation methods.

[0004] The objective of this invention is achieved through the following technical solution:

[0005] A method for calculating yaw distance based on great circle projection, implemented by an airborne embedded device, is described below:

[0006] Step 1: Input the latitude and longitude of the starting point Or, the ending point D, and the current position P of the current flight segment. Use the great circle projection algorithm to solve for the arc lengths of OrD, OrP, and PD. Then calculate the angle OrOD. Finally, calculate the straight line lengths of OrD, OrP, and PD.

[0007] Step 2: Intersect the great circle that passes through point P and is perpendicular to the great circle defined by points Or, D, and O with the arc OrD. Set the intersection point as T1. Connect point T1 and point O with a straight line. The intersection point of the straight line T1O and the straight line OrD is T.

[0008] Step 3: Using the Law of Cosines, find the measure of the three angles of triangle OrPD; using the angle TDP and the length of line PD, find the lengths of lines TP and DT.

[0009] Step 4: In triangle OrDO, find the angle of OrDO using the lengths of lines OrO, OD, and OrD and the Law of Cosines. Since angle OrDO is equal to angle TDO, in triangle DTO, find the length of line TO using the Law of Cosines and the lengths of lines TDO, DT, and OD.

[0010] Step 5: In triangle TPO, calculate the angle TOP using the lengths of lines TO, TP, and PO, as well as the law of cosines. Multiply this angle by the Earth's radius to get the length of arc T1P, which is the yaw distance.

[0011] Preferably, before the eccentricity calculation begins, the latitude and longitude of the input current segment start point Or, segment end point D, and aircraft current position point P are judged. If the absolute value of any longitude data is greater than 180.0 degrees or the absolute value of any latitude data is greater than 90.0 degrees, the calculation is terminated. If the aircraft position is outside the segment range, the calculation is terminated.

[0012] The beneficial effects of this invention are as follows:

[0013] This invention provides a method for calculating yaw distance based on great circle projection. The calculation results are more accurate than various approximate yaw distance algorithms. This algorithm is computationally simple, has minimal impact on system performance, and is suitable for widespread use in embedded real-time systems or simulation systems. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of an algorithm for calculating yaw distance based on great circle projection. Detailed Implementation

[0015] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0016] like Figure 1 As shown, assuming the Earth's center point is O, the flight segment runs from the starting point Or to the ending point D, and the aircraft's position is point P, then the latitude and longitude data of points Or, D, and P are given. Assuming the great circle tangent passing through point P and perpendicular to the ODOr plane intersects the great circle arc OrD at point T1, then the length of the arc PT1 is the required yaw distance.

[0017] A method for calculating yaw distance based on great circle projection, implemented by an airborne embedded device, is described below:

[0018] Step 1: Input the latitude and longitude of the starting point Or, the ending point D, and the current position P of the current flight segment. Use the great circle projection algorithm to solve for the arc lengths of OrD, OrP, and PD. Then calculate the angle OrOD. Finally, calculate the straight line lengths of OrD, OrP, and PD.

[0019] Step 2: Intersect the great circle that passes through point P and is perpendicular to the great circle determined by points Or, D, and O with the arc OrD. Set the intersection point as T1. Connect point T1 and point O with a straight line. Assume that the intersection point of the straight line T1O and the straight line OrD is T. Then the straight line TP is perpendicular to the straight line OrD (they are the projections of planes OPT1 and ODOr onto PDOr, respectively).

[0020] Step 3: Using the Law of Cosines, find the measures of the three angles of triangle OrPD; using the angle TDP and the length of line PD, find the lengths of lines TP and DT.

[0021] Step 4: In triangle OrDO, the lengths of lines OrO and OD are equal to the Earth's radius. Using the length of line OrD from Step 1 and the Law of Cosines, we can find the angle OrDO. Since angle OrDO is equal to angle TDO, in triangle DTO, using the Law of Cosines, we can find the length of line TO by using angle TDO, the length of line DT (obtained in Step 3), and the length of line OD (Earth's radius).

[0022] Step 5: In triangle TPO, the lengths of the three lines TO, TP and PO are known. Then, according to the law of cosines, the angle TOP can be calculated. Multiplying this angle by the Earth's radius gives the length of the arc T1P, which is the yaw distance.

[0023] To improve the robustness of the algorithm, before the off-range calculation begins, the latitude and longitude of the input current segment start point Or, segment end point D, and aircraft current position point P can be judged. If the absolute value of any longitude data is greater than 180.0 degrees or the absolute value of any latitude data is greater than 90.0 degrees, the calculation will be terminated. If the aircraft position is outside the segment range, the calculation will also be terminated.

[0024] The data used in this method are shown in Table 1:

[0025] Table 1. Data used in the calculation process.

[0026] a_OrOD double Figure 1 The value of the median angle OrOD in radians a_OrOP double Figure 1 The value of the median angle OrOP in radians. a_DOP double Figure 1 The value of the median angle DOP in radians a_OrDP double Figure 1 The value of the median angle OrDP in radians a_TOP double Figure 1 The value of the median angle TOP, in radians l_OrD float Figure 1 The value of the midline segment OrD, in meters. l_OrP float Figure 1 The value of the median segment OrP, in meters. l_PD float Figure 1 The value of the midline segment PD, in meters arc_OrD float Figure 1 The OrD value of the middle arc segment, in meters. arc_OrP float Figure 1 The value of OrP for the middle arc segment, in meters. arc_PD float Figure 1 The value of PD for the middle arc segment, in meters. l_TD float Figure 1 The value of the middle segment TD, in meters l_TP float Figure 1 The value of the midline segment TP, in meters. l_TO float Figure 1 The value of the midline segment TO, in meters. a_OrDO double Figure 1 The value of the median angle OrDO in radians. theta1 double The aircraft's bearing relative to the starting point, in radians. Theta2 double The orientation of the endpoint relative to the starting point, in radians.

[0027] The execution process of this calculation method can be described using C-style PDL:

[0028] if (the absolute value of any input longitude data is greater than 180.0 degrees or the absolute value of latitude data is greater than 90.0 degrees)

[0029] return -1;

[0030] if (the aircraft's position is outside the flight segment range)

[0031] return-2;

[0032] Convert the input latitude and longitude data from degrees to radians;

[0033] The arc_OrD was calculated using the large circle projection method.

[0034] The arc_OrP was calculated using the large circle projection method.

[0035] arc_PD was calculated using the large circle projection method.

[0036] Calculate the value of angle a_OrOD;

[0037] Calculate the value of angle a_OrOP;

[0038] Calculate the value of angle a_DOP;

[0039] Calculate the value of line segment l_OrD;

[0040] Calculate the value of line segment l_OrP;

[0041] Calculate the value of line segment l_PD;

[0042] Use the law of cosines to calculate the value of angle a_OrDP;

[0043] Calculate the length of line segment l_TP;

[0044] Calculate the length of line segment l_TD;

[0045] Calculate the value of angle a_OrDO;

[0046] Use the law of cosines to calculate the length of line segment l_TO;

[0047] Use the law of cosines to calculate the value of angle a_TOP;

[0048] Calculate the yaw rate and store it in *ctd;

[0049] Determine the yaw direction based on theta1 and theta2;

[0050] return 1.

[0051] It is understood that those skilled in the art can make equivalent substitutions or modifications to the technical solution and inventive concept of the present invention, and all such substitutions or modifications should fall within the protection scope of the appended claims.

Claims

1. A great circle projection based off-distance calculation method, implemented by an on-board embedded device, characterized in that The solution process is as follows: Step 1: Input the latitude and longitude of the starting point Or, the ending point D, and the current position P of the current flight segment. Use the great circle projection algorithm to solve for the arc lengths of OrD, OrP, and PD. Then calculate the angle OrOD. Finally, calculate the straight line lengths of OrD, OrP, and PD. Step 2: Intersect the great circle that passes through point P and is perpendicular to the great circle defined by points Or, D, and O with the arc OrD. Set the intersection point as T1. Connect point T1 and point O with a straight line. The intersection point of the straight line T1O and the straight line OrD is T. Step 3: Using the Law of Cosines, find the measure of the three angles of triangle OrPD; using the angle TDP and the length of line PD, find the lengths of lines TP and DT. Step 4: In triangle OrDO, find the angle of OrDO using the lengths of lines OrO, OD, and OrD and the Law of Cosines. Since angle OrDO is equal to angle TDO, in triangle DTO, find the length of line TO using the Law of Cosines and the lengths of lines TDO, DT, and OD. Step 5: In triangle TPO, calculate the angle TOP using the lengths of lines TO, TP, and PO, as well as the law of cosines. Multiply this angle by the Earth's radius to get the length of arc T1P, which is the yaw distance.

2. The method for calculating yaw distance based on great circle projection according to claim 1, characterized in that... Before the yaw calculation begins, the latitude and longitude of the input current segment start point Or, segment end point D, and aircraft current position point P are judged. If the absolute value of any longitude data is greater than 180.0 degrees or the absolute value of any latitude data is greater than 90.0 degrees, the calculation is terminated. If the aircraft position is outside the segment range, the calculation is terminated.

Images