High latitude unified coordinate system construction and navigation parameter expression method

Abstract

The application belongs to the technical field of navigation, and specifically discloses a high-latitude space-time reference unified coordinate system construction and navigation parameter expression method, which comprises the following steps: based on the current geographical latitude continuously monitored by a navigation system, whether a high latitude is reached is determined by comparing the current geographical latitude with a high-latitude threshold; if yes, the following steps of the high-latitude mode are executed: based on an internal calculation coordinate system of the navigation system in the high-latitude mode, navigation parameters are calculated; based on the conversion relationship between the internal calculation coordinate system and a grid coordinate system, the navigation parameters in the internal calculation coordinate system are converted into the navigation parameters in the grid coordinate system; and through the external interface of the navigation system, the navigation parameters in the grid coordinate system are uniformly output externally. The application provides a high-latitude space-time reference unified coordinate system, guarantees the stability of the heading indication, is compatible with the internal calculation coordinate systems of various navigation systems, and outputs the navigation parameters in a unified navigation parameter expression mode.

Description

Technical Field

[0001] This application belongs to the field of navigation technology, and more specifically, relates to a method for constructing a unified coordinate system for high-latitude spatiotemporal reference and expressing navigation parameters. Background Technology

[0002] Existing navigation systems in low and mid-latitude regions mainly use a geographic coordinate system (latitude) based on the CGCS2000 coordinate system. ,longitude Elevation ) and ECEF geocentric rectangular coordinate system (Earth coordinate system, , , ( ) is used for positioning, orientation, and speed measurement. Although both are two ways of expressing the same coordinate system, they are applicable to different inertial spaces in practical applications—the geographic coordinate system is generally the g system, while the ECEF coordinate system is generally the e system. There are differences in inertial navigation arrangement, so they should be distinguished.

[0003] However, in high-latitude regions, due to the sharp convergence of the Earth's meridians, the definition of "true north" in traditional geographic coordinate systems tends to become invalid, leading to the following problems.

[0004] (1) Inaccurate heading indication: Traditional heading angles are not defined near the poles (North Pole or South Pole), which seriously affects navigation safety.

[0005] (2) Location representation is not intuitive: Traditional latitude and longitude are greatly distorted at high latitudes, which is not conducive to nautical chart operations and situational understanding.

[0006] (3) Poor system compatibility: Different navigation devices (such as inertial navigation, satellite navigation, and electronic chart systems) may adopt different temporary correction schemes at high latitudes, resulting in inconsistent output information and difficulty in data fusion.

[0007] While there are some local solutions such as grid navigation and lateral navigation, they are all isolated applications. There is a lack of a complete and standardized coordinate system to systematically solve the above problems, and a complete technical chain from the definition of the basic coordinate system to the expression of navigation parameters and the unified output of multiple systems has not yet been formed. Summary of the Invention

[0008] To address the shortcomings of existing technologies, the purpose of this application is to provide a unified coordinate system for high-latitude spatiotemporal reference, ensuring stable heading indication, compatibility with the internal solution coordinate system of various navigation systems, and outputting navigation parameters in a unified way, thereby achieving high stability, wide compatibility, and standardization of high-latitude navigation operations.

[0009] To achieve the above objectives, in a first aspect, this application provides a method for constructing a unified coordinate system for high-latitude spatiotemporal reference and expressing navigation parameters, the method comprising: Based on the current geographic latitude continuously monitored by the navigation system, the system compares the current geographic latitude with a high-latitude threshold to determine whether it is in a high-latitude region. If so, the following steps for high-latitude mode are executed: Based on the internal coordinate system of the navigation system in high-latitude mode, the navigation parameters are calculated; Based on the transformation relationship between the internal solution coordinate system and the grid coordinate system, the navigation parameters in the internal solution coordinate system are converted into navigation parameters in the grid coordinate system; Through the external interface of the navigation system, navigation parameters in the grid coordinate system are uniformly output to the outside world; The unified coordinate system for high-latitude spatiotemporal reference is constructed based on multiple internal solution coordinate systems applicable to the internal calculation of navigation parameters in high-latitude modes, a grid coordinate system for unified output of navigation parameters, and the transformation relationship between the internal solution coordinate system and the grid coordinate system.

[0010] It can be understood that this application continuously monitors the current geographical latitude and compares it with a high-latitude threshold. After entering the high-latitude mode, it allows different types of navigation systems (inertial navigation, satellite navigation, celestial navigation, etc.) to select a suitable internal calculation coordinate system (inertial coordinate system, earth coordinate system, geographic coordinate system, grid coordinate system, lateral coordinate system, wandering azimuth coordinate system, etc.) for internal calculation based on their respective error characteristics. This avoids the problem of calculation overflow or accuracy reduction caused by using a single coordinate system. After the internal calculation is completed, the navigation parameters under each internal calculation coordinate system are uniformly converted to the grid coordinate system through a standardized coordinate transformation relationship, which is compatible with the internal calculation coordinate systems of various navigation systems and achieves broad compatibility of high-latitude navigation operations.

[0011] In the grid coordinate system, grid north is a fixed reference direction defined parallel to the prime meridian. It is clearly defined across the entire latitude range (including the poles), thus fundamentally solving the problem of the traditional true north direction being undefined near the poles, ensuring stable heading indication, and achieving high stability in high-latitude navigation operations.

[0012] Using the grid north as a stable reference, the system outputs heading, speed, and position parameters in a unified manner to achieve standardization of high-latitude navigation operations.

[0013] Therefore, the method for constructing a unified coordinate system for high-latitude spatiotemporal reference and expressing navigation parameters provided in this application can achieve high stability, wide compatibility and standardization in high-latitude navigation operations.

[0014] In one possible implementation, the multiple internal solution coordinate systems include at least two of the following coordinate systems: inertial coordinate system, geographic coordinate system, earth coordinate system, grid coordinate system, transverse earth coordinate system, transverse geographic coordinate system, and wandering azimuth coordinate system.

[0015] Definition of a grid coordinate system: using a point on the Earth's ellipsoid as a reference point. axis, shaft and The axis is drawn from the reference point. axis, shaft and The axes form a right-handed rectangular coordinate system; The axis (north axis of the grid) points north along the intersection of the grid plane and the tangent plane of the meridian. The axis (zenith axis) points vertically upward along the direction of the outward normal of the meridian plane; The axis is determined by the right-hand rule; The coordinate system is the grid coordinate system.

[0016] Definition of the transverse Earth coordinate system: The axis points from the Earth's center to the North Pole; The axis points from the Earth's center to the intersection of the Greenwich Meridian and the equator (i.e., the equator point of the traditional Prime Meridian). The axis points from the Earth's center to the intersection of the 90° East meridian and the equator (the transverse North Pole). axis, shaft and The axes form a right-handed rectangular coordinate system, with the three axes originating from the Earth's center. The coordinate system is the horizontal Earth coordinate system.

[0017] Definition of a horizontal geographic coordinate system: using a point on the Earth's ellipsoid as a reference point. axis, shaft and The axis is drawn from the reference point. axis, shaft and The axes form a right-handed rectangular coordinate system; The axis extends horizontally along the tangent direction (lateral eastward) of the auxiliary latitude circle (or auxiliary transverse latitude circle) at the reference point; The axis is perpendicular to the outer normal of the ellipsoid at the reference point, pointing vertically upwards (towards the zenith). The axis is determined by the right-hand rule; The coordinate system is the horizontal geographic coordinate system.

[0018] Definition of a wandering azimuth coordinate system: using a point on the Earth's ellipsoid as a reference point. axis, shaft and The axis is drawn from the reference point. axis, shaft and The axes form a right-handed rectangular coordinate system. The axis deviates from geographic north (true north) by an azimuth angle in the horizontal plane. The direction of the angle The axis points towards the zenith along the direction of the outward normal to the Earth's ellipsoid at the reference point. The axis is determined by the right-hand rule; The coordinate system is the wander azimuth coordinate system. The wander azimuth angle changes with the movement of the vehicle.

[0019] In one possible implementation, the transformation relationship between the inertial coordinate system and the grid coordinate system is based on the transformation relationship between the inertial coordinate system and the Earth coordinate system, as well as the transformation relationship between the Earth coordinate system and the grid coordinate system. It is certain; The transformation relationship between geographic coordinate systems and grid coordinate systems is achieved through the following transformation matrix ( ) Definitely: ; Transformation matrix This represents the transformation relationship between geographic coordinate systems and grid coordinate systems. Indicates grid deflection angle; The transformation relationship between the Earth coordinate system and the grid coordinate system is determined by the following formula: ; Transformation matrix Transformation matrix represents the transformation relationship between the Earth coordinate system and the grid coordinate system. This represents the transformation relationship between the Earth coordinate system and the geographic coordinate system; The transformation relationship between the horizontal geographic coordinate system and the grid coordinate system is expressed by the following transformation matrix ( ) Definitely: ; Transformation matrix This represents the transformation relationship between the horizontal geographic coordinate system and the grid coordinate system; The transformation relationship between the horizontal Earth coordinate system and the grid coordinate system is determined by the following formula: ; Transformation matrix Transformation matrix represents the transformation relationship between the horizontal Earth coordinate system and the grid coordinate system. This represents the transformation relationship between the horizontal Earth coordinate system and the geographic coordinate system; The transformation relationship between the wandering azimuth coordinate system and the grid coordinate system is achieved through the wandering azimuth angle ( Transform the attitude matrix from the wandering azimuth coordinate system to the geographic coordinate system, and then... The coordinates are determined by transformation to a grid coordinate system.

[0020] In one possible implementation, the azimuth angle is shifted. The rate of change is determined by the following formula: ; in, Indicates the rate of change of the wandering azimuth angle. Indicates the rate of change of geographical longitude. This represents the geographical latitude; by integrating the above equation, the wandering azimuth angle can be obtained. .

[0021] In one possible implementation, auxiliary lateral latitude is used in the position update step calculated within the lateral coordinate system (lateral Earth coordinate system or lateral geographic coordinate system). Replacing horizontal latitude To calculate the radius of curvature of the ramustralis in the transverse coordinate system. (and ellipsoid curvature parameters); auxiliary lateral latitude Determined by the following formula: ; in, Represented in CGCS2000 Cartesian coordinate system Coordinate components; Indicates the semi-major axis of the reference ellipsoid; lateral latitude With auxiliary lateral latitude The conversion relationship between them is as follows: ; in, Indicates geographical latitude; Indicates geographical longitude; Indicates horizontal latitude; Indicates lateral longitude; This represents the first eccentricity of the reference ellipsoid.

[0022] Specifically, a transverse latitude is an irregular closed curve formed by all points with the same transverse latitude on the Earth's ellipsoid, and its curvature parameter is complex to calculate. An auxiliary transverse latitude, on the other hand, is an equipotential ellipse obtained by a plane parallel to the transverse equatorial plane cutting across the Earth's ellipsoid; it has a regular shape and its corresponding auxiliary transverse latitude... It can be determined by simple conversion relationships ( This is obtained by using auxiliary lateral latitude in the location update equation. Replacing horizontal latitude Calculate the radius of curvature of the zonal loop. The addition of coordinate components can greatly simplify the calculation process, making the position integral more numerically stable and effectively reducing the computational complexity of navigation solutions in high-latitude lateral coordinate systems. When accurate results are required, the conversion relationship between lateral latitude and auxiliary lateral latitude can be used for compensation and correction to ensure the accuracy of the solution.

[0023] In one possible implementation, the navigation parameters include: position parameters, heading parameters, speed parameters, and time parameters; Location parameters include geographic latitude and longitude ( , ) and lateral latitude and longitude ( , ).

[0024] In one possible implementation, the conversion formula between geographic latitude and longitude and lateral latitude and longitude is as follows: ; in, Indicates geographical latitude; Indicates geographical longitude; Indicates horizontal latitude; Indicates lateral longitude.

[0025] In one possible implementation, the high-latitude threshold includes a high-latitude entry threshold. (Typical value is 75°) and high-latitude exit threshold (Typical value is 70°) and It is a positive value, and ; The above determination of whether it is located at a high latitude includes: Continuously monitor geographical latitude through navigation system And determine whether to switch modes based on the hysteresis judgment mechanism: when Exceed When, the navigation system switches to high-latitude mode; when Down to The navigation system will exit high-latitude mode at the following time.

[0026] Specifically, near high-latitude boundaries, if only a single threshold is used for mode switching, the vehicle will frequently trigger mode switching (i.e., "jittering") when it fluctuates slightly around the threshold, affecting navigation accuracy and system stability. This application addresses this by setting a high-latitude entry threshold. (Typical value 75°) and exit threshold The difference (approximately 5°) between the typical value of 70° and the threshold forms a hysteresis interval, giving mode switching a certain inertia: the vehicle must actually descend below 70° to exit high-latitude mode, rather than simply oscillating back and forth at the 75° threshold to trigger repeated switching. The choice of the 75° entry threshold is based on the fact that in areas above 75° North (or South) latitude, the convergence of Earth's meridians has caused significant error accumulation and calculation overflow risks at the algorithm level due to the traditional geographic north direction. Therefore, an alternative coordinate system is needed for internal calculation. The setting of the hysteresis interval (70°~75°) effectively prevents frequent mode jitter near high-latitude boundaries while ensuring the timeliness of switching, thus improving the overall stability and robustness of the navigation system in high-latitude entry and exit scenarios.

[0027] One possible implementation also includes: When supporting multiple navigation systems, the single-process conversion time, calculation accuracy, and calculation stability of each navigation system in different high-latitude regions are pre-collected. Upon determining the location to be at a high latitude, based on the pre-collected data, the current high-latitude region, and the optimization objective, the optimal navigation system is selected from among the multiple systems as the target navigation system for navigation operations. The optimization objective is determined using the following objective function: ; in: This represents the objective function value, used to comprehensively evaluate the overall performance of the navigation system in the current high-latitude region. A larger value indicates better overall performance. This represents the single calculation and conversion time of the navigation system in the current high-latitude region (unit: ms). The smaller the value, the higher the calculation efficiency. This represents the accuracy score of the navigation system in the current high-latitude region (normalized dimensionless quantity, value range). A larger value indicates higher solution accuracy; This represents the solution stability score of the navigation system in the current high-latitude region (normalized dimensionless quantity, value range). A larger value indicates better solution stability; , and The weighting coefficients corresponding to solution efficiency, solution accuracy, and solution stability respectively (satisfying) The configuration can be adjusted to prioritize efficiency, accuracy, and stability according to specific application scenarios.

[0028] Specifically, based on the objective function, when determining to enter the high-latitude mode, the objective function value is calculated for all supported navigation systems. Select The navigation system with the highest value is selected as the target navigation system to ensure that the optimal navigation system is continuously used in different high-latitude regions, taking into account the efficiency, accuracy and stability of navigation operations.

[0029] It is understandable that different types of navigation systems (inertial navigation, satellite navigation, celestial navigation, etc.) exhibit varying computational performance in different high-latitude regions, and simply using a single navigation system cannot achieve optimal performance in all high-latitude areas. This application establishes a performance database by pre-collecting performance data of various navigation systems in different high-latitude regions. Upon entering high-latitude mode, it uses an objective function to comprehensively score each candidate navigation system based on the specific high-latitude region currently in use, dynamically selecting the navigation system with the best overall performance for navigation operations. The objective function comprehensively considers three dimensions: computational efficiency (measured by the reciprocal of the single computation conversion time), computational accuracy, and computational stability. It also supports flexible configuration for different application scenarios (e.g., prioritizing efficiency in high-real-time scenarios, and prioritizing accuracy in high-precision measurement scenarios) through weighting coefficients. This achieves optimal overall efficiency, accuracy, and stability in high-latitude navigation operations at the system level, solving the performance limitations caused by the fixed use of a single coordinate system or navigation system in existing solutions.

[0030] One possible implementation also includes using a suboptimal navigation system to perform navigation operations in the event of a failure of the optimal navigation system.

[0031] Specifically, when the target navigation system (target function value) When the largest navigation system fails, the target function value is recalculated from the remaining available navigation systems. Sort the navigation system by size from largest to smallest, select the navigation system with the largest current objective function value (i.e., the original suboptimal navigation system) as the new target navigation system, and continue to execute the navigation solution and parameter output workflow in the high-latitude mode.

[0032] It is understandable that in complex high-latitude environments, a single navigation system may fail due to hardware malfunctions, signal blockage, or external interference. If the system lacks a fault-handling mechanism, navigation service interruption will occur, severely impacting the safety of high-latitude operations. This application maintains a performance ranking list of multiple navigation systems. When the current target navigation system fails, it can quickly degrade to a suboptimal navigation system with minimal switching costs to continue providing navigation services, ensuring the continuity and reliability of high-latitude navigation operations. Simultaneously, fault switching still follows the objective function priority ranking, ensuring that the solution with the relatively optimal overall performance is always selected within the range of available navigation systems, preventing a blind reduction in navigation operation quality due to fault switching, demonstrating the system's robustness and fault tolerance.

[0033] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art.

[0034] (1) Solved the high-latitude heading problem: By introducing stable benchmarks such as "grid north", the heading has a clear and continuous definition in the entire latitude range (including the pole), which effectively eliminates the problem of inaccurate heading indication caused by the lack of definition of the traditional true north near the pole.

[0035] (2) It realizes the unification and standardization of navigation parameters: it provides a unique and accurate way to express all navigation information such as position, heading, and speed in high-latitude regions. Through the grid coordinate system output mechanism, it is compatible with sensors of different navigation devices (inertial navigation, satellite navigation, astronomical navigation, etc.), providing a foundation for multi-source data fusion.

[0036] (3) Improved system compatibility and flexibility: The internal solution can use the coordinate system most suitable for the characteristics of the algorithm (inertial coordinate system, earth coordinate system, geographic coordinate system, grid coordinate system, horizontal coordinate system, wandering coordinate system, etc.), while the external output is uniformly in grid coordinate system format, which takes into account both computational performance and system compatibility.

[0037] (4) A complete technology chain is provided: For the "high-latitude mode", this application has formed a complete workflow of internal solution coordinate system selection → solution process → parameter conversion → grid coordinate system output, which solves the defects of isolated application and lack of systematicness of existing solutions. Attached Figure Description

[0038] Figure 1 This is an overview diagram of the unified coordinate system for high-latitude spatiotemporal reference provided in the embodiments of this application; Figure 2 This is a schematic diagram of the grid coordinate system provided in the embodiments of this application; Figure 3 This is a schematic diagram of the horizontal Earth coordinate system provided in the embodiments of this application; Figure 4 This is a schematic diagram of the horizontal geographic coordinate system provided in the embodiments of this application; Figure 5 This is a schematic diagram of the transverse latitude line provided in the embodiments of this application; Figure 6 This is a schematic diagram of the wandering orientation coordinate system provided in the embodiments of this application. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0040] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0041] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, multiple elements means two or more elements, etc.

[0042] First, the technical terms involved in the embodiments of this application will be introduced.

[0043] High-latitude regions: High-latitude regions are an important concept in geography, generally referring to the areas on the Earth's surface between 60° north and south latitude and the poles (90° north and south latitude).

[0044] CGCS2000 (China Geodetic Coordinate System 2000): A geocentric coordinate reference frame highly compatible with WGS-84. It uses the Earth's center as the origin, with the z-axis pointing to the North Pole, the x-axis pointing to the intersection of the Greenwich Meridian and the equator, and the y-axis forming a right-handed coordinate system with the x and z axes.

[0045] Geographic Coordinate System (g-system): Based on the CGCS2000 coordinate system, it is a local geographic coordinate system with a point on the Earth's ellipsoid as the origin, and the geographic north (true north), true east, and zenith direction as the y, x, and z axes, respectively. It is the most commonly used reference coordinate system in low- and mid-latitude navigation, but it cannot be directly used in high-latitude regions because "true north" becomes ineffective.

[0046] The ECEF (Earth-Centered Earth-Fixed Coordinate System, e-frame) is a rectangular coordinate system with the Earth's center as its origin and that rotates with the Earth. The x-axis points to the intersection of the Greenwich Meridian and the equator, the z-axis points to the North Pole, and the y-axis, together with x and z, forms a right-handed coordinate system, namely the Earth coordinate system (e-system). Both the x-axis and the geographic coordinate system are based on CGCS2000.

[0047] True North: refers to the direction of the Earth's North Pole, which is the reference direction for defining heading in traditional geographic coordinate systems. In high-latitude regions (especially near the poles), meridians converge sharply, and the direction of true north tends to be singular or undefined, making it impossible to indicate in traditional heading systems.

[0048] The Prime Meridian: The meridian plane with a longitude of 0° passing through the Greenwich Observatory, is the reference plane defining the north direction of the grid in the grid coordinate system. The grid plane in the grid coordinate system is parallel to the Prime Meridian.

[0049] Lateral coordinate system: The transverse North Pole (the intersection of the 90°E meridian and the equator) is used instead of the traditional geographic North Pole as the reference pole, including two forms: the transverse Earth coordinate system and the transverse geographic coordinate system. Inertial navigation systems using the transverse coordinate system can avoid the overflow phenomenon in polar region calculations.

[0050] Transverse North Pole: The reference pole used in the transverse coordinate system, located at the intersection of the 90° East meridian and the equator. The corresponding transverse South Pole is located at the intersection of the 90° West meridian and the equator.

[0051] Auxiliary transverse parallels: These are equipotential ellipses (cross-sectional ellipses) formed by planes parallel to the transverse equatorial plane cutting across the Earth's ellipsoid; they are regular elliptical curves. Unlike transverse parallels (irregular curves), auxiliary transverse parallels are easier to calculate mathematically and are used to define transverse geographic coordinate systems. Axial direction.

[0052] Lateral latitude: The angle between the normal to the outside of the ellipsoid at any point on the ellipsoid and the transverse equatorial plane, denoted as . .

[0053] Lateral longitude: The location parameter corresponding to geographic longitude in a lateral coordinate system, denoted as... .

[0054] Radius of curvature of the lateral axis: In the transverse coordinate system, the radius of curvature of the Earth ellipsoid along the transverse normal section is denoted as . .

[0055] Inertial navigation system: A navigation system that uses gyroscopes and accelerometers to calculate the position, velocity, and attitude of a vehicle by integrating motion parameters.

[0056] Strapdown inertial navigation system: a type of inertial navigation system in which sensors (gyroscopes and accelerometers) are directly fixed to the carrier without physical platform isolation.

[0057] Astronomical navigation system: A system that uses celestial position information for positioning and navigation.

[0058] Internal calculation coordinate system: The coordinate system used by the navigation system for navigation calculation. It can be flexibly selected according to the error characteristics of each navigation device (such as inertial coordinate system, earth coordinate system, geographic coordinate system, grid coordinate system, lateral coordinate system, wandering coordinate system, etc.).

[0059] External output coordinate system: The unified coordinate system used by the navigation system when outputting and displaying navigation information to the outside world.

[0060] The embodiments of this application are described below with reference to the accompanying drawings.

[0061] Example 1: Construction of a unified coordinate system for high-latitude spatiotemporal reference and definition of navigation parameters.

[0062] This embodiment provides a complete high-latitude navigation solution, aiming to construct a hierarchical coordinate system and uniformly define all navigation parameters based on it. Specifically, it consists of four parts: constructing a unified high-latitude spatiotemporal reference coordinate system, defining high-latitude navigation parameters, establishing transformation formulas between coordinate systems, and providing a coordinate system selection scheme for the navigation system.

[0063] (i) Construct a unified coordinate system for high-latitude spatiotemporal reference.

[0064] The unified coordinate system for high-latitude spatiotemporal reference is mainly used for internal calculations in high-latitude navigation systems, including grid coordinate systems and transverse coordinate systems.

[0065] 1. Grid coordinate system.

[0066] The grid coordinate system is constructed as follows: In the CGCS2000 coordinate system, a grid plane is defined parallel to the prime meridian. The intersection of the grid plane and the tangent plane of the prime meridian is defined as the grid north direction. Axis; the outward normal of the meridional plane is axis; shaft and shaft and The axes form a right-handed rectangular coordinate system. This is how the coordinate system is obtained. The coordinate system is the grid coordinate system.

[0067] Figure 2 This is a schematic diagram of a grid coordinate system. Figure 2 The Earth ellipsoid is shown at the center, with three coordinate axes derived from a reference point M on the Earth's surface: The axis (north axis of the grid) points north along the intersection of the grid plane and the tangent plane of the meridian. The axis (zenith axis) points vertically upward along the direction of the outward normal of the meridian plane; The east-facing axis (the grid's eastward axis) forms a right-handed rectangular coordinate system with the previous two axes, pointing eastward along the grid. For example... Figure 2As shown, the grid north direction is a fixed reference direction defined by the prime meridian, and there is a grid deflection angle between it and the local true north direction. .

[0068] Since the grid north direction is a fixed definition of north, the inertial navigation system replaces the traditional pole direction with the grid north direction in the high-latitude solution process, thereby solving the solution overflow problem caused by the divergence of the true north direction.

[0069] 2. Horizontal coordinate system.

[0070] The horizontal coordinate system includes the horizontal Earth coordinate system and the horizontal geographic coordinate system, both of which are based on the CGCS2000 coordinate system definition.

[0071] (1) Horizontal Earth Coordinate System: The intersection of the 90° East meridian and the equator is the transverse North Pole, and the intersection of the 90° West meridian and the equator is the transverse South Pole; the origin is at the Earth's center, defined as follows: The axis points to the North Pole. The axis points to the intersection of the Greenwich Meridian and the equator. The axis points to the transverse North Pole. shaft and shaft and The axes form a right-handed rectangular coordinate system, from which the following is obtained The coordinate system is the horizontal Earth coordinate system.

[0072] Figure 3 This is a schematic diagram of a horizontal Earth coordinate system. Figure 3 The Earth's ellipsoid is shown at the center, with the origin of the coordinate system located at the Earth's center: The axis points from the Earth's center to the traditional North Pole; The axis points from the Earth's center to the intersection of the Greenwich Meridian and the equator (i.e., the equator point of the traditional Prime Meridian). The axes point from the Earth's center to the intersection of the 90° East meridian and the equator (the transverse North Pole). The three axes satisfy the right-hand rule. For example... Figure 3 As shown, the horizontal coordinate system defines the transverse North Pole on the equator, thus making the traditional high-latitude region equivalent to the mid-to-low latitude region in the horizontal coordinate system, avoiding the singularity problem of the solution near the pole.

[0073] (2) Lateral geographic coordinate system: Based on the CGCS2000 coordinate system, the lateral Earth coordinate system is defined by cutting the Earth ellipsoid with a plane parallel to the lateral equatorial plane to form an equipotential ellipse, thus obtaining auxiliary latitude circles; with a certain point on the Earth ellipsoid as the origin, the coordinate system is defined as follows: The axis points laterally eastward along the tangent of the auxiliary latitude circle at that point. The axis, along the normal to the Earth's ellipsoid at that point, points towards the zenith. axis, shaft and The axes satisfy the right-hand rectangular coordinate system, thus obtaining... The coordinate system is the horizontal geographic coordinate system of that point.

[0074] Figure 4 This is a schematic diagram of a horizontal geographic coordinate system. Figure 4 A local coordinate system is established with a point M on the ellipsoid as the origin: The axis extends horizontally along the tangent direction (eastward) of the auxiliary latitude circle (or auxiliary transverse latitude circle) at that point; The axis points vertically upwards along the outer normal of the ellipsoid at that point (in the zenith direction); The axis (horizontal north) is determined by the right-hand rule. Figure 4 The text also indicates horizontal latitude. The geometric meaning of is the angle between the external normal of the ellipsoid of point M and the transverse equatorial plane.

[0075] When inertial navigation systems use a lateral coordinate system for calculations at high latitudes, the overflow phenomenon near the poles is avoided by using lateral poles instead of traditional poles.

[0076] In a horizontal geographic coordinate system, the horizontal latitude of any point M on the ellipsoid is defined. Let be the angle between the normal to the outside of the ellipsoid at this point and the transverse equatorial plane. Let the CGCS2000 rectangular coordinates of any point be... Then the ellipsoidal normal vector coordinates at that point are (CGCS2000 coordinate system). The lateral latitude of this point satisfies equation (1), which, combined with the equation of the Earth ellipsoid, yields the equation of the lateral latitude as equation (2).

[0077] (1); Parameter explanation: Lateral latitude, which is the angle between the outer normal of the ellipsoid at a point on the ellipsoid and the transverse equatorial plane; , , The three coordinate components of this point in the CGCS2000 rectangular coordinate system (Earth coordinate system); The first eccentricity of the CGCS2000 reference ellipsoid.

[0078] (2); Parameter explanation: : The semi-major axis of the CGCS2000 reference ellipsoid; : The minor semi-axis of the CGCS2000 reference ellipsoid; , , , , The meaning is the same as in formula (1).

[0079] A horizontal parallel of latitude is an irregular curve, such as... Figure 5 As shown. To facilitate calculations, auxiliary horizontal latitude lines are defined.

[0080] Figure 5 This is a schematic diagram of a horizontal latitude line. Figure 5 The diagram shows the same lateral latitude on the Earth's ellipsoid. The curve formed by all the points (lateral parallels of latitude) is an irregular closed curve (a non-equipotential ellipse); in contrast, the equipotential ellipse (auxiliary parallels of latitude) obtained by cutting the ellipsoid with a plane parallel to the transverse equatorial plane has a regular shape. (Auxiliary transverse latitude) Defined by equation (3), and compared with the true lateral latitude The relationship is shown in equation (5).

[0081] Auxiliary lateral latitude The definition formula is Equation (3), and the equation of the auxiliary transverse latitude line is Equation (4).

[0082] (3); Parameter explanation: : Auxiliary horizontal latitude is for horizontal latitude An approximate expression for this is the angle between the plane containing the equipotential ellipse and the transverse equatorial plane. : The y-coordinate components of this point in the CGCS2000 rectangular coordinate system; : CGCS2000 reference ellipsoid semi-major axis.

[0083] (4); Parameter explanation: : Auxiliary horizontal latitude, with the same meaning as in formula (3); , , The three coordinate components of this point in the CGCS2000 rectangular coordinate system; , : The major and minor axes of the CGCS2000 reference ellipsoid.

[0084] The auxiliary lateral latitude is an equipotential ellipse, formed by a plane parallel to the lateral equatorial plane cutting through the Earth's ellipsoid. Its regular shape facilitates subsequent navigation calculations. The relationship between the lateral latitude and the auxiliary lateral latitude is given by equation (5).

[0085] (5); Parameter explanation: : Auxiliary horizontal latitude, with the same meaning as in formula (3); Geographical latitude (traditional latitude); Geographic longitude (traditional longitude); : Horizontal latitude, with the same meaning as in formula (1); : Lateral longitude (longitude of the vehicle in the lateral coordinate system); : First eccentricity of the CGCS2000 reference ellipsoid.

[0086] 3. Wandering azimuth coordinate system.

[0087] The wandering azimuth coordinate system is constructed as follows: Under the geographic coordinate system based on the CGCS2000 coordinate system, a point on the Earth's ellipsoid is taken as the origin, and a coordinate system is defined as follows: The axis represents the azimuth angle along the point in the horizontal plane that deviates from geographic north (true north). The direction of the angle (counterclockwise is positive), The formula for calculating the angle is shown in equation (6). The axis points towards the zenith along the direction of the outward normal to the Earth's ellipsoid at that point. axis, shaft and The axes form a right-handed rectangular coordinate system, from which the following is obtained The coordinate system is the wandering coordinate system of that point.

[0088] Figure 6 This is a schematic diagram of the wandering azimuth coordinate system. Figure 6 A local coordinate system is established with a point on the ellipsoid as the origin: The axis lies in the horizontal plane, and its direction is deflected and shifted relative to geographic north (true north) by an azimuth angle. (Counterclockwise is positive), and it changes slowly as the carrier moves; The axis is vertically upward (in the zenith direction); The axis is determined by the right-hand rule.

[0089] Wandering azimuth angle The formula for the rate of change is equation (6).

[0090] (6); Parameter explanation: : Rate of change of wander azimuth angle (unit: rad / s); Rate of change of geographical longitude (unit: rad / s), i.e., the rate of change of the longitude of the carrier; : The geographical latitude of the current point.

[0091] (ii) Define high-latitude navigation parameters.

[0092] It is recommended that high-latitude navigation parameters be output within a grid coordinate system framework: firstly, this avoids overflow during high-latitude navigation parameter calculation; secondly, the conversion between grid coordinate systems and geographic coordinate systems is simple, and the latitude and longitude remain unchanged after conversion. The high-latitude navigation parameters are redefined below.

[0093] (1) High-latitude location: High-latitude location is represented by latitude and longitude in the CGCS2000 coordinate system (geographic coordinate system). If the inertial navigation system uses lateral arrangement calculation, lateral longitude can be added for the lateral coordinate system. and horizontal latitude As a supplementary expression for high-latitude locations, the conversion formula between geographical latitude and longitude and lateral latitude and longitude is Equation (7).

[0094] (7); Parameter explanation: Geographical latitude; Geographical longitude; : Horizontal latitude, with the same meaning as in formula (1); : Lateral longitude (longitude coordinates of the vehicle in the lateral coordinate system).

[0095] (2) High-latitude heading: The high-latitude heading output in the grid coordinate system includes the high-latitude carrier heading, high-latitude carrier track direction, high-latitude wind direction and high-latitude current direction. The north of the grid is used as the heading reference, and the eastward axis of the grid is the positive direction.

[0096] (3) High-latitude velocity: The relative velocity of the carrier at high latitudes is represented by decomposing velocity components in the grid coordinate system. The motion component along the eastward axis of the grid is called the eastward grid velocity, and the motion component along the northward axis of the grid is called the northward grid velocity.

[0097] (4) High-latitude time: Coordinated Universal Time (UTC) is used as the high-latitude time reference to ensure that the time reference is not affected by changes in geographical location and to facilitate the synchronization and fusion of data from multiple systems.

[0098] (III) Conversion formula for the unified coordinate system of high-latitude spatiotemporal reference.

[0099] This section presents the transformation relationships between various coordinate systems and the grid coordinate system, providing a complete mathematical basis for parameter transformation between different internal solution coordinate systems and the unified output coordinate system of the navigation system.

[0100] 1. Conversion between geographic coordinate system and grid coordinate system.

[0101] The transformation matrix between the geographic coordinate system and the grid coordinate system is shown in equation (8).

[0102] (8); Parameter explanation: : Coordinate transformation matrix from geographic coordinate system (g system) to grid coordinate system (G system); : Grid deflection angle, which is the angle between the grid north direction and the geographic north direction (true north) (see equation (18) for the specific expression).

[0103] 2. Conversion between Earth coordinate system (ECEF) and grid coordinate system.

[0104] The transformation relationship between the Earth coordinate system (ECEF) and the grid coordinate system is shown in equation (9).

[0105] (9); Parameter explanation: : Coordinate transformation matrix from Earth coordinate system (e-frame) to grid coordinate system (G-frame); The transformation matrix from the geographic coordinate system (g system) to the grid coordinate system (G system) is shown in equation (8); The transformation matrix from the Earth coordinate system (e-system) to the geographic coordinate system (g-system) is shown in equation (13). : Grid deflection angle, see equation (18); Geographical latitude; Geographical longitude.

[0106] 3. Conversion between horizontal geographic coordinate system and grid coordinate system.

[0107] The transformation relationship between the horizontal geographic coordinate system and the grid coordinate system is shown in equation (10).

[0108] (10); Parameter explanation: From the horizontal geographic coordinate system ( The coordinate transformation matrix from the grid coordinate system (G system) to the lattice coordinate system (G system). This matrix is ​​a constant matrix that does not change with the location of the carrier, reflecting the fixed geometric relationship between the lattice coordinate system and the lateral geographic coordinate system.

[0109] 4. Transformation between the horizontal Earth coordinate system and the grid coordinate system.

[0110] The transformation relationship between the horizontal Earth coordinate system and the grid coordinate system is shown in equation (11).

[0111] (11); Parameter explanation: From the horizontal Earth coordinate system ( The coordinate transformation matrix from the grid coordinate system (G system) to the grid coordinate system (G system); : The transformation matrix from the horizontal Earth coordinate system to the geographic coordinate system is shown in equation (13); , , The meaning is the same as in formula (9).

[0112] 5. Conversion between Earth coordinate system and transverse Earth coordinate system.

[0113] The transformation relationship between the Earth coordinate system and the transverse Earth coordinate system is shown in equation (12).

[0114] (12); Parameter explanation: From the horizontal Earth coordinate system ( The coordinate transformation matrix from the geocentric coordinate system (e-system) to the Earth coordinate system (e-system). This matrix is ​​also a constant matrix, reflecting the fixed rotational relationship between the two geocentric rectangular coordinate systems.

[0115] 6. Conversion between horizontal Earth coordinate system and geographic coordinate system.

[0116] The transformation relationship between the horizontal Earth coordinate system and the geographic coordinate system is shown in equation (13), where This is the transformation matrix from the Earth coordinate system to the geographic coordinate system.

[0117] (13); Parameter explanation: : Coordinate transformation matrix from horizontal Earth coordinate system to geographic coordinate system; Transformation matrix from Earth coordinate system (e-frame) to geographic coordinate system (g-frame); ; :The transformation matrix from the horizontal Earth coordinate system to the Earth coordinate system is shown in equation (12); Geographical latitude; Geographical longitude.

[0118] 7. Conversion between horizontal geographic coordinate system and horizontal Earth coordinate system.

[0119] The rectangular coordinates and the geodetic coordinates are interchanged through the horizontal latitude and longitude. The relationship between the rectangular coordinate components and the horizontal latitude and longitude is shown in equation (14).

[0120] (14); Parameter explanation: , , The three rectangular coordinate components of a point in the horizontal Earth coordinate system; : Radius of curvature of the zonal circle (radius of the zonal circle), the specific calculation formula is shown in equation (15); : Horizontal latitude, with the same meaning as in formula (1); : Lateral longitude; : First eccentricity of the CGCS2000 reference ellipsoid.

[0121] In equation (14), the radius of curvature of the zonal loop is... The calculation formula is Equation (15).

[0122] (15); Parameter explanation: : The radius of curvature of the ramusoidal circle in the transverse coordinate system, used for the calculation of the coordinate components in equation (14); : The semi-major axis of the CGCS2000 reference ellipsoid; First eccentricity of the CGCS2000 reference ellipsoid; : Lateral latitude; : Lateral longitude.

[0123] Similarly, the transformation matrix between the horizontal Earth coordinate system and the horizontal geographic coordinate system can be expressed as equation (16).

[0124] (16); Parameter explanation: From the horizontal Earth coordinate system ( From the horizontal geographic coordinate system to the horizontal geographic coordinate system The coordinate transformation matrix of the system; : Horizontal latitude, with the same meaning as in formula (1); : Lateral longitude.

[0125] 8. Rotation of the geographic coordinate system relative to the horizontal geographic coordinate system and grid deflection.

[0126] Assume the geographic coordinate system rotates relative to the horizontal geographic coordinate system. The angle (i.e., grid deflection angle) and the transformation matrix are shown in equation (17).

[0127] (17); Parameter explanation: : Grid deflection , where is the rotation angle, and is the rotation matrix of the geographic coordinate system relative to the horizontal geographic coordinate system; : Grid deflection angle, which is the angle between the grid north direction and the geographic north direction (true north), is expressed in geographic latitude and longitude by equation (18).

[0128] Grid deflection The formula expressed in terms of geographical latitude and longitude is Equation (18).

[0129] (18); Parameter explanation: Grid deflection angle: The angle between the grid north direction and the geographic north direction (true north); Geographical latitude; Geographical longitude.

[0130] (iv) Selection of high-latitude coordinate system.

[0131] When navigation systems perform calculations and outputs at high latitudes, they can be divided into internal calculation coordinate systems and external output coordinate systems, depending on the usage scenario.

[0132] When multiple navigation devices or systems within a system need to output and display high-latitude navigation information, a grid coordinate system should be used as the unified output coordinate system. Using a grid heading system can solve the problems of lost geographic north and inability to indicate headings at high latitudes, while maintaining consistency between latitude and longitude information and the CGCS2000 coordinate system, thus not affecting the usability of latitude and longitude positions.

[0133] Different navigation systems can employ different types of internal navigation calculation coordinate systems. During navigation calculation, a suitable coordinate system can be selected as the internal navigation calculation coordinate system based on the different latitude-related error characteristics of navigation systems such as inertial navigation systems, celestial navigation systems, and strapdown systems. These coordinate systems include inertial coordinate systems, Earth coordinate systems, geographic coordinate systems, grid coordinate systems, lateral coordinate systems, and wandering coordinate systems. When displaying system parameters on navigation equipment, a coordinate system transformation is performed to uniformly output the data to the grid coordinate system.

[0134] In summary, Figure 1 An overview of the unified coordinate system for high-latitude spatiotemporal reference is presented, demonstrating the hierarchical relationships and transformation paths between the various coordinate systems.

[0135] like Figure 1 As shown, for the CGCS2000 reference coordinate system, the Earth coordinate system (ECEF / e system) and the geographic coordinate system (g system) are branched out from it; in the high-latitude navigation layer, the grid coordinate system (G system) is located in the central position as the unified output coordinate system, and is connected to the g system through equation (8), to the e system through equation (9), and to the horizontal geographic coordinate system through equation (10). (system) connection, through equation (11) and the transverse Earth coordinate system ( (System) connection; the wandering azimuth coordinate system (w system) is connected through the grid deflection angle. (Equations (17) to (18)) are related to the g system.

[0136] Example 2: The workflow of the navigation system in high-latitude mode.

[0137] This embodiment describes the specific implementation of the workflow after the navigation system enters "high-latitude mode," which involves selecting the internal coordinate system, performing the calculation process, parameter transformation, and outputting the grid coordinate system. The coordinate system definitions, transformation formulas, and parameter definitions used in this embodiment are in accordance with Embodiment 1.

[0138] 1. Conditions for switching to high-latitude mode.

[0139] The navigation system continuously monitors the latitude and geography of the current location. And determine whether to switch to high-latitude mode based on the following principles.

[0140] (1) Conditions for entering the high-latitude mode: when the absolute value of geographic latitude is Exceeding the entry threshold (The typical value is 75°, which can be adjusted according to the specific needs of the system.) When this value is reached, the navigation system switches to high-latitude mode, activating the workflow described in this embodiment. The selection of the switching threshold of 75° is based on the fact that in areas above 75° North (or South) latitude, the convergence of the Earth's meridians has caused significant error accumulation and calculation overflow risks at the algorithm level for the traditional geographical north direction, necessitating the use of an alternative coordinate system for internal calculation.

[0141] (2) Conditions for exiting high-latitude mode: To avoid frequent mode switching (i.e., "jitter") near the threshold, the system adopts a hysteresis mechanism: when the absolute value of the geographic latitude is... Drop to the exit threshold (Typical value is 70°, which satisfies) The navigation system can only exit high-latitude mode and revert to traditional geographic coordinate system navigation parameter output when the following conditions are met. During the switching process, the system maintains the continuity of navigation parameters and avoids abrupt changes in output through a smooth transition between coordinate systems.

[0142] 2. Selection of internal solution coordinate system.

[0143] Based on the type and error characteristics of current navigation systems, and by analyzing the applicability of various coordinate systems in high-latitude regions, the internal solution coordinate system selected for this navigation calculation is determined. The selected internal solution coordinate system can be one or more of the following coordinate systems.

[0144] (1) Inertial coordinate system (i-system): suitable for high-precision inertial navigation systems (such as platform-type inertial navigation). This coordinate system is not directly coupled with latitude and can be stably solved in the entire latitude range. However, the solution results of the inertial coordinate system need to be converted to the Earth coordinate system through the Earth's rotation angular rate, and then converted to the grid coordinate system for output.

[0145] (2) Earth coordinate system (e-frame / ECEF): Applicable to satellite navigation systems and inertial navigation systems based on the geocentric coordinate system. The origin of the Earth coordinate system is at the Earth's center, and the three coordinate axes are fixed to the Earth. After the calculation is completed, it is obtained through equation (9) (i.e. Convert navigation parameters to grid coordinate system output.

[0146] (3) Geographic coordinate system (g system): Suitable for navigation systems with high accuracy requirements in low and medium latitudes, and which have already adopted the geographic coordinate system for arrangement before entering high latitudes. When continuing to use the internal calculation of the geographic coordinate system in high latitudes, it is necessary to use grid deflection compensation (equation (18)) to control the heading error, and output it through equation (8) (i.e. Transform to a grid coordinate system.

[0147] (4) Grid coordinate system (G system): suitable for systems that directly use grid north as the reference direction for attitude calculation (such as grid-arranged strapdown inertial navigation). This coordinate system directly replaces true north with grid north, and no additional grid deflection compensation is required in high-latitude calculations. Moreover, the internal calculation coordinate system is consistent with the output coordinate system, and the parameter transformation is the simplest.

[0148] (5) Horizontal coordinate system System and (System): An inertial navigation system suitable for navigation in high latitudes and even polar regions (latitude close to 90°). The transverse coordinate system uses 90°E as the transverse north pole, mapping high-latitude regions to mid-to-low latitude regions under the transverse coordinate system, which can effectively eliminate the problem of solution overflow. After the solution is completed, it is obtained through equation (10) (i.e. ) or formula (11) (i.e. Convert to grid coordinate system for output.

[0149] (6) Wandering azimuth coordinate system (w system): Applicable to strapdown inertial navigation systems, it allows the coordinate axes to wander in the horizontal plane by azimuth angle. (Equation (6)) Free drift avoids the exacerbation of compass effect and gyro torque saturation problems caused by meridian convergence at high latitudes. After the solution is completed, the azimuth angle is first shifted. (Obtained by integrating equation (6)) and establishing a connection with the geographic coordinate system, then through (Equation (8)) is converted to grid coordinate system for output.

[0150] 3. Solution process.

[0151] Based on the selected internal solution coordinate system, navigation calculations are completed in the selected coordinate system through inertial navigation arrangement equations (attitude update, velocity update, position update) to obtain navigation parameters (heading, velocity, position) expressed in the selected internal solution coordinate system.

[0152] Taking the horizontal coordinate system as an example, the steps of the solution process are as follows.

[0153] Step 1: Based on the angular rate and specific force information output by the inertial measurement unit (IMU), obtain the attitude matrix of the carrier in the lateral coordinate system through the attitude differential equation in the lateral geographic coordinate system. (Transformation matrix from the carrier coordinate system to the horizontal geographic coordinate system).

[0154] Step 2: Based on the pose matrix obtained in Step 1 And the IMU comparison output, through the velocity differential equation in the lateral geographic coordinate system, obtains the velocity vector of the vehicle in the lateral geographic coordinate system. (Eastward component) and northward component ).

[0155] Step 3: Based on the velocity vector obtained in Step 2 By using the position differential equation in the horizontal coordinate system (in terms of horizontal latitude and longitude) , (Expression), the integral obtains the position of the carrier in the horizontal coordinate system (horizontal longitude). and horizontal latitude In this step, the auxiliary transverse latitude line plays a key role (see “5. The role of the auxiliary transverse latitude line in the workflow” in this embodiment).

[0156] 4. Parameter transformation (internal solution coordinate system → grid coordinate system).

[0157] Based on the navigation parameters (heading, velocity, position) obtained in the internal solution coordinate system through the above calculation process, the navigation parameters in the grid coordinate system are obtained through the corresponding coordinate system transformation formulas and used as the external output. The parameter transformation methods for various internal solution coordinate systems are explained below.

[0158] 4.1 Heading parameter conversion.

[0159] High-latitude headings are defined with grid north as the reference, and the conversion method varies depending on the internal solution coordinate system.

[0160] (1) When the internal solution coordinate system is the geographic coordinate system (g system): use equation (8) (transformation matrix) Add the grid deflection angle to the internally calculated geographic heading angle. (Equation (18)) to obtain the grid heading angle. Grid deflection angle The sign depends on the current geographical latitude and longitude, which is precisely given by equation (18).

[0161] (2) When the internal solution coordinate system is the Earth coordinate system (e-system): first through (Equation (13)) transforms the e-system attitude matrix to the g-system, and then through (Equation (8)) is transformed to the grid coordinate system, and the grid heading angle is extracted, which is equivalent to directly using (Equation (9)).

[0162] (3) When the internal solution coordinate system is the grid coordinate system (G system): the internal solution is performed directly in the grid system without additional heading transformation, and the grid heading angle is directly extracted from the attitude matrix.

[0163] (4) The internal solution coordinate system is the horizontal geographic coordinate system. (System) When: Through Equation (10) transforms the attitude matrix of the lateral geographic system to the grid coordinate system. Since Equation (10) is a constant matrix, the transformation process is simple and the grid heading angle can be directly extracted from the transformed attitude matrix.

[0164] (5) The internal solution coordinate system is the transverse Earth coordinate system. (System) When: Through (Equation (11)) transforms the horizontal Earth system attitude matrix to the grid coordinate system and extracts the grid heading angle.

[0165] (6) When the internal solution coordinate system is a wandering azimuth coordinate system (w system): first pass through the wandering azimuth angle (Obtained by integrating equation (6)) The w-system attitude matrix is ​​restored to the geographic coordinate system (g-system), and then through... (Equation (8)) is converted to the grid coordinate system to extract the grid heading angle.

[0166] 4.2 Speed ​​parameter conversion.

[0167] High-latitude velocities are expressed using the eastward and northward components of the grid. The conversion method is as follows.

[0168] (1) When the internal solution coordinate system is the geographic coordinate system (g system): the geographic velocity vector (eastward velocity) is converted to the geographic coordinate system (g system). Northbound speed )pass Transform (Equation (8)) to the grid coordinate system to obtain the eastward velocity of the grid. Northbound speed of grid .

[0169] (2) When the internal solution coordinate system is the Earth coordinate system (e-frame): the velocity vector of the e-frame is passed through... Transform (Equation (9)) to the grid coordinate system and extract the grid eastward velocity and grid northward velocity.

[0170] (3) When the internal solution coordinate system is the grid coordinate system (G system): the velocity vector obtained by the internal solution has been directly expressed in the grid coordinate system, and no coordinate transformation is required. It can be directly used as the output quantity.

[0171] (4) The internal solution coordinate system is the horizontal geographic coordinate system. When considering the lateral geographic system velocity vector (lateral eastward velocity), the following applies: Lateral northward speed )pass Transform (Equation (10)) to the grid coordinate system to obtain the grid velocity components.

[0172] (5) The internal solution coordinate system is the transverse Earth coordinate system. When the Earth system velocity vector is passed through the system: Transform (Equation (11)) to the grid coordinate system to obtain the grid velocity components.

[0173] (6) When the internal solution coordinate system is a wandering azimuth coordinate system (w system): the velocity vector of the w system is first passed through the wandering azimuth angle. Returning to the geography department, and then through Transform (Equation (8)) to the grid coordinate system to obtain the grid velocity components.

[0174] 4.3 Position parameter conversion.

[0175] High-latitude locations are defined by geographical latitude and longitude ( , The primary output format is , supplemented by horizontal latitude and longitude ( , (As a supplement, the position conversion method is as follows.)

[0176] (1) When the internal solution coordinate system is the Earth coordinate system (e-system) or the geographic coordinate system (g-system): the geographic latitude and longitude are directly obtained from the internal solution. , ), which can be directly used as the location output in the grid coordinate system (the grid coordinate system and the geographic coordinate system are consistent in the location expression, and the latitude and longitude remain unchanged).

[0177] (2) When the internal solution coordinate system is a grid coordinate system (G system): Since the location information of the grid coordinate system and the geographic coordinate system is equivalent, the location obtained by the internal solution is directly output as the geographic latitude and longitude, without the need for additional conversion.

[0178] (3) The internal solution coordinate system is a horizontal coordinate system (horizontal geographic coordinate system). Earth coordinate system or horizontal Earth coordinate system When calculating the latitude and longitude, the internal solution directly yields the lateral latitude and longitude. , The latitude and longitude need to be converted to geographic latitude and longitude using equation (7) (conversion formula between geographic latitude and longitude and lateral latitude and longitude). , Output after ( ). At the same time, horizontal latitude and longitude ( , It can also be used as supplementary information for high-latitude locations and output to the outside world.

[0179] (4) When the internal solution coordinate system is a wandering azimuth coordinate system (w system): the wandering azimuth coordinate system is based on the geographic coordinate system, and the location information itself is based on geographic latitude and longitude ( , It is maintained in a grid coordinate system and can be directly used as the position output in the grid coordinate system without the need for additional position coordinate transformation.

[0180] 5. The role of auxiliary horizontal latitude lines in the workflow.

[0181] The auxiliary transverse latitude line (defined by equations (3) to (5)) plays a key role in step three (position update) of the "solution process" in the above workflow. Its specific uses and functions are as follows.

[0182] (1) Application: In the position differential equation in the transverse coordinate system, it is necessary to calculate the radius of curvature of the maxima and minima in the transverse coordinate system. (Equation (15)) and the corresponding ellipsoid curvature parameters, these parameters are related to the auxiliary lateral latitude (Equation (3)) is directly related. Because the actual transverse latitude is an irregular curve (such as...) Figure 5 As shown in the figure, the curvature parameter calculation is complex; the auxiliary transverse latitude line is an equipotential ellipse (i.e. an ellipse obtained by cutting an ellipsoid with a plane parallel to the transverse equatorial plane), which is simple to calculate and has a regular form.

[0183] (2) Specific usage: In the location update equation, auxiliary lateral latitude is used. Replacing actual horizontal latitude This allows for the calculation of ellipsoid curvature parameters, thus significantly simplifying the calculation of equations (14) (transformation between the transverse Earth coordinate system and the transverse geographic coordinate system) and (15) (radius of curvature of the ramusoidal orbit). (True transverse latitude) With auxiliary lateral latitude The precise conversion relationship between them is given by equation (5), which can be compensated and corrected when precise results are required.

[0184] (3) Function: The introduction of auxiliary lateral latitude lines makes the position integral calculation more numerically stable, effectively reducing the computational complexity of navigation solution in high-latitude lateral coordinate system. It is an important simplification method for the engineering implementation of the solution scheme inside the lateral coordinate system.

[0185] 6. Output of grid coordinate system.

[0186] Based on the heading, velocity, and position parameters in the grid coordinate system obtained through the above parameter transformation steps, the navigation system acquires and outputs the grid coordinate system navigation parameters externally through its external interface (such as a serial port protocol or digital bus), completing the entire workflow from internal calculation to unified grid output in high-latitude mode. Specific outputs include: (1) Grid heading: The high-latitude heading angle (including carrier heading, track heading, wind direction, current direction, etc.) with grid north as the reference, in degrees (°); (2) Grid velocity: Grid eastward velocity Northbound speed of grid The unit is m / s; (3) Location: Geographical latitude and longitude ( , It is consistent with the CGCS2000 coordinate system, and the unit is degrees (°); when using the internal calculation of the transverse coordinate system, the transverse latitude and longitude can be output as well ( , ); (4) Time: Coordinated Universal Time (UTC), consistent with the time base of high latitudes.

[0187] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0188] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A high-latitude spatio-temporal reference unified coordinate system construction and navigation parameter expression method, characterized in that, include: Based on the current geographic latitude continuously monitored by the navigation system, the system compares the current geographic latitude with a high-latitude threshold to determine whether it is in a high-latitude region. If so, the following steps for high-latitude mode are executed: Based on the internal coordinate system of the navigation system in high-latitude mode, the navigation parameters are calculated; Based on the transformation relationship between the internal solution coordinate system and the grid coordinate system, the navigation parameters in the internal solution coordinate system are converted into navigation parameters in the grid coordinate system; Through the external interface of the navigation system, navigation parameters in the grid coordinate system are uniformly output to the outside world; The unified coordinate system for high-latitude spatiotemporal reference is constructed based on multiple internal solution coordinate systems applicable to the internal solution of navigation parameters in high-latitude modes, a grid coordinate system for unified output of navigation parameters, and the transformation relationship between the internal solution coordinate system and the grid coordinate system. In the position updating step solved in the transverse coordinate system, the auxiliary transverse latitude is used instead of the transverse latitude to calculate the radius of curvature of the orthodrome in the transverse coordinate system ; the auxiliary transverse latitude is determined from the following equation: ； wherein, represents the coordinates in the CGCS2000 rectangular coordinate system coordinate components; represents the reference ellipsoid long semi-axis; transverse latitude The conversion relationship between the auxiliary transverse latitude is: ； wherein, represents geographic latitude; represents geographic longitude; represents transverse latitude; represents transverse longitude; represents the first eccentricity of the reference ellipsoid.

2. The method of claim 1, wherein the method further comprises: determining a time interval between the first time and the second time; and determining a time interval between the third time and the fourth time. Multiple internal solution coordinate systems include at least two of the following coordinate systems: inertial coordinate system, geographic coordinate system, earth coordinate system, grid coordinate system, transverse earth coordinate system, transverse geographic coordinate system, and wandering azimuth coordinate system.

3. The method of claim 2, wherein the method further comprises: determining a time interval between the first time and the second time; and determining a time interval between the third time and the fourth time. The transformation relationship between the inertial coordinate system and the grid coordinate system is determined based on the transformation relationship between the inertial coordinate system and the Earth coordinate system, as well as the transformation relationship between the Earth coordinate system and the grid coordinate system. The transformation relationship between the geographic coordinate system and the grid coordinate system is determined by the following transformation matrix: ； conversion matrix represents the conversion relationship between the geographic coordinate system and the grid coordinate system, represents the grid deflection angle; The transformation relationship between the Earth coordinate system and the grid coordinate system is determined by the following formula: ； conversion matrix represents a conversion relationship between the earth coordinate system and the grid coordinate system; conversion matrix represents a conversion relationship between the earth coordinate system and the geographic coordinate system; The transformation relationship between the horizontal geographic coordinate system and the grid coordinate system is determined by the following transformation matrix: ； Transformation matrix This represents the transformation relationship between the horizontal geographic coordinate system and the grid coordinate system; The transformation relationship between the horizontal Earth coordinate system and the grid coordinate system is determined by the following formula: ； Transformation matrix Transformation matrix represents the transformation relationship between the horizontal Earth coordinate system and the grid coordinate system. This represents the transformation relationship between the horizontal Earth coordinate system and the geographic coordinate system; The transformation relationship between the wandering azimuth coordinate system and the grid coordinate system is achieved by transforming the attitude matrix in the wandering azimuth coordinate system to the geographic coordinate system through the wandering azimuth angle, and then through... The coordinates are determined by transformation to a grid coordinate system.

4. The method for constructing a unified coordinate system for high-latitude spatiotemporal reference and expressing navigation parameters according to claim 3, characterized in that, Wandering azimuth angle The rate of change is determined by the following formula: ； in, Indicates the rate of change of the wandering azimuth angle. Indicates the rate of change of geographical longitude. This represents the geographical latitude. Integrating the above equation yields the wander azimuth angle. .

5. The method for constructing a unified coordinate system for high-latitude spatiotemporal reference and expressing navigation parameters according to claim 1, characterized in that, Navigation parameters include: position parameters, heading parameters, speed parameters, and time parameters; The location parameters include geographic latitude and longitude and lateral latitude and longitude.

6. The method for constructing a unified coordinate system for high-latitude spatiotemporal reference and expressing navigation parameters according to claim 5, characterized in that, The conversion formula between geographical latitude and longitude and lateral latitude and longitude is as follows: ； in, Indicates geographical latitude; Indicates geographical longitude; Indicates horizontal latitude; Indicates lateral longitude.

7. The method for constructing a unified coordinate system for high-latitude spatiotemporal reference and expressing navigation parameters according to claim 1, characterized in that, High-latitude thresholds include high-latitude entry thresholds. and high-latitude exit threshold , and It is a positive value, and ; The determination of whether it is at a high latitude includes: Continuously monitor geographical latitude through navigation system And determine whether to switch modes based on the hysteresis judgment mechanism: when Exceed When, the navigation system switches to high-latitude mode; when Down to The navigation system will exit high-latitude mode at the following time.

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