Transmitting system strapdown inertial navigation method based on Lie group / Lie algebra

Abstract

The invention particularly relates to a transmitting system strapdown inertial navigation method based on Lie group / Lie algebra. The method comprises the following steps: constructing a navigation kinematics model corresponding to an aircraft; wherein the navigation kinematics model is used for representing a strapdown inertial navigation model of the aircraft according to the position, speed and attitude characteristics of the aircraft under a launching coordinate system; establishing a corresponding Lie group differential equation for the navigation kinematics model based on Lie group representation of aircraft motion; wherein the Lie group corresponding to the movement of the aircraft represents that a special European group is utilized to incorporate the attitude, speed and position characteristics of the aircraft; acquiring inertial measurement unit IMU parameters corresponding to the current data processing cycle of the aircraft; discretizing the Lie group differential equation, and solving the discretized Lie group differential equation by using the IMU parameter corresponding to the current data processing cycle to obtain update data of attitude, position and speed of the aircraft. According to the method, the linear motion and the angular motion of the carrier are integrally modeled, and the calculation precision of a numerical value updating algorithm is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of inertial navigation, and in particular to a strapdown inertial navigation method of a transmitting system based on Lie group / Lie algebra. Background Art

[0002] In related technologies, the function of the strapdown inertial navigation algorithm is to numerically integrate the output information of the gyroscope and accelerometer to obtain attitude, velocity, and position information. It is the core algorithm of the strapdown inertial navigation system. The accuracy of the next generation of inertial devices is expected to increase by one to two orders of magnitude compared to the accuracy of current inertial-grade devices, so the requirements for the accuracy of the inertial navigation algorithm are also increasing. In traditional algorithms, quaternions are used to describe angular motion, while the attitude information in the description of linear motion is represented by the direction cosine matrix; the attitude update uses the series expansion method, and the velocity update uses the step-by-step integration method. The design of the separate attitude and velocity update processes brings difficulties to the design of higher-precision numerical update algorithms.

[0003] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present invention, and therefore may include information that does not constitute prior art known to ordinary technicians in this field. Summary of the Invention

[0004] The present invention provides a launch system strapdown inertial navigation method based on Lie groups / Lie algebras, a storage medium, a computer program product, and an electronic device. In the design of a navigation algorithm, the linear motion and angular motion of a carrier are integratedly modeled. Under the same mathematical structure, the numerical update problem of the carrier's attitude, velocity, and position is processed, thereby improving compensation accuracy and overcoming the defects in the prior art to a certain extent.

[0005] Other features and advantages of the present invention will become apparent from the following detailed description, or may be learned in part by practice of the present invention.

[0006] According to a first aspect of the present invention, there is provided a transmission system strapdown inertial navigation method based on Lie groups / Lie algebras, the method comprising:

[0007] Constructing a navigation kinematic model corresponding to the aircraft; wherein the navigation kinematic model is used to represent the aircraft's strapdown inertial navigation model based on the aircraft's position, velocity, and attitude characteristics in the launch coordinate system;

[0008] Based on the Lie group representation of aircraft motion, the corresponding Lie group differential equations are established for the navigation kinematic model. The Lie group representation of aircraft motion incorporates the attitude, velocity, and position characteristics of the aircraft using a special Euclidean group.

[0009] Get the IMU parameters corresponding to the current data processing cycle of the aircraft;

[0010] The Lie group differential equation is discretized and solved using the IMU parameters corresponding to the current data processing cycle to obtain updated data on the aircraft's attitude, position, and velocity.

[0011] In some exemplary embodiments, constructing a navigation kinematic model corresponding to the aircraft includes:

[0012] Define the launch coordinate system corresponding to the aircraft; where the origin of the launch coordinate system is O g The launch point is the launch point, with the x-axis pointing in the launch aiming direction in the horizontal plane of the launch point, the y-axis pointing upward perpendicular to the horizontal plane of the launch point, and the z-axis, x-axis, and y-axis forming a right-handed rectangular coordinate system. The launch coordinate system is fixed to the Earth, and the positional relationship between the launch coordinate system and the Earth is determined based on the geographic latitude B0, longitude λ0, altitude h0, and launch azimuth A0 of the launch point.

[0013] A launch inertial coordinate system is defined based on the launch coordinate system; wherein the launch inertial coordinate system coincides with the launch coordinate system at the moment of launch of the aircraft;

[0014] Define the carrier coordinate system corresponding to the aircraft; where the carrier coordinate system origin is at the center of mass of the aircraft, the x-axis coincides with the longitudinal axis of the aircraft, the y-axis is located in the longitudinal symmetry plane of the aircraft and is perpendicular to the x-axis, and the z-axis forms a right-handed rectangular coordinate system with the x-axis and y-axis;

[0015] Configure the corresponding transformation matrix based on the launch inertial coordinate system and the carrier coordinate system

[0016] According to the position, velocity, attitude characteristics and coordinate system transformation matrix of the aircraft in the launch coordinate system Construct the navigation kinematic model corresponding to the aircraft, including:

[0017]

[0018] Among them, V g is the velocity in the launch coordinate system, f b is the specific force of the added output value in the carrier coordinate system, g g is the gravity in the launch coordinate system; in, is the angular velocity of the carrier coordinate system relative to the launch coordinate system; is the angular velocity of the Earth's rotation; P g is the position in the launch coordinate system.

[0019] In some exemplary embodiments, the method further comprises:

[0020] Based on the attitude characteristics of the aircraft, a special orthogonal group SO(3) is configured, and the corresponding Lie algebra is configured as well as

[0021] According to the special orthogonal group and the speed characteristics of the aircraft, configure the special Euclidean group SE(3); and configure the corresponding Lie algebra

[0022] According to the mapping relationship between Lie group and Lie algebra, combined with the transformation relationship between the launch inertial coordinate system and the carrier coordinate system, the Lie algebra is determined. The exponential mapping relationship between the special orthogonal group SO(3);

[0023] Based on Lie algebra The exponential mapping relationship between the special orthogonal group SO(3) and the special Euclidean group SE(3) is determined. The index mapping relationship between them.

[0024] In some exemplary embodiments, based on the Lie group representation of the aircraft motion, a corresponding Lie group differential equation is established for the navigation kinematics model, including:

[0025] Based on the navigation kinematic model of the aircraft, the special Euclidean group SE(3) and Lie algebra The exponential mapping relationship between them configures the Lie group differential equation: in, is the Lie algebra of the Lie group Y, V=(v;ω) T ∈se(3); v is the velocity, ω is the angular velocity.

[0026] In some exemplary embodiments, the discretizing the Lie group differential equation and solving the discretized Lie group differential equation using IMU parameters corresponding to the current data processing cycle to obtain updated data on the attitude, position, and velocity of the aircraft includes:

[0027] The discretized Lie group differential equation is updated to obtain the spiral Lie algebra from the carrier coordinate system to the launch coordinate system. The spiral Lie algebra includes the attitude characteristics, velocity characteristics, and position characteristics of the aircraft.

[0028] Based on the spiral Lie algebra, the Lie group variables are updated, the IMU parameters are substituted, and the earth's gravity, angular velocity, and the drag velocity caused by the earth's rotation are compensated to solve the increments of attitude, velocity, and position to complete the data update of the attitude, velocity, and position information in the launch coordinate system.

[0029] In some exemplary embodiments, the IMU parameters include: angular velocity and specific force of the aircraft;

[0030] The method further comprises:

[0031] A velocity parameter corresponding to the specific force is determined, so as to be used for bringing the velocity parameter into the Lie group variable.

[0032] In some exemplary embodiments, the current data processing cycle includes a plurality of consecutive sampling points;

[0033] The method further comprises:

[0034] The increments of the IMU parameters of multiple sampling points are accumulated, and the accumulated IMU parameter increments are configured as the IMU parameters corresponding to the current data processing cycle.

[0035] According to a second aspect of the present invention, a computer program product is provided, on which a computer program is stored. When the computer program is executed by a processor, the above-mentioned transmitting system strapdown inertial navigation method based on Lie group / Lie algebra is implemented.

[0036] According to a third aspect of the present invention, there is provided a storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the computer program implements the above-mentioned transmitting system strapdown inertial navigation method based on Lie groups / Lie algebras.

[0037] According to a fourth aspect of the present invention, there is provided an electronic device, comprising:

[0038] processor; and

[0039] a memory for storing executable instructions of the processor;

[0040] Wherein, the processor is configured to implement the above-mentioned transmitting system strapdown inertial navigation method based on Lie group / Lie algebra by executing the executable instructions.

[0041] The embodiment of the present invention provides a launch system strapdown inertial navigation method based on Lie group / Lie algebra, which integrates the linear motion and angular motion of the aircraft into a model, incorporates the rotation and translation differential equations of the carrier into a special Euclidean group SE(3) to form a new differential equation, and performs motion solving under this mathematical structure, thereby being able to handle the numerical update problem of the attitude, velocity and position of the aircraft under the same model structure, thereby achieving the purpose of improving the calculation accuracy of the numerical update algorithm.

[0042] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] The accompanying drawings are incorporated into and constitute a part of this specification, illustrate embodiments consistent with the present invention, and together with the description, serve to explain the principles of the present invention. Obviously, the drawings described below are only some embodiments of the present invention, and it is clear that those skilled in the art can derive other drawings based on these drawings without inventive effort.

[0044] Figure 1 A schematic diagram schematically illustrates a transmitting system strapdown inertial navigation method based on Lie groups / Lie algebras according to an exemplary embodiment of the present invention;

[0045] Figure 2 A schematic diagram schematically illustrating a relationship between a transmitting coordinate system and an Earth-centered Earth-fixed coordinate system according to an exemplary embodiment of the present invention;

[0046] Figure 3 A schematic diagram schematically illustrating a relationship between a Lie group and a Lie algebra according to an exemplary embodiment of the present invention;

[0047] Figure 4 A schematic diagram schematically illustrates a process flow of a transmitting system strapdown inertial navigation method based on Lie groups / Lie algebras according to an exemplary embodiment of the present invention;

[0048] Figure 5 A schematic diagram schematically illustrates an algorithm flow of a transmitting system strapdown inertial navigation method based on Lie groups / Lie algebras according to an exemplary embodiment of the present invention;

[0049] Figure 6 The figure schematically shows the composition of an electronic device in an exemplary embodiment of the present invention. DETAILED DESCRIPTION

[0050] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be embodied in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete and will fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0051] In addition, the accompanying drawings are merely schematic illustrations of the present invention and are not necessarily drawn to scale. Identical reference numerals in the figures denote identical or similar parts, and thus repetitive descriptions thereof will be omitted. Some of the blocks shown in the accompanying drawings are functional entities that do not necessarily correspond to physically or logically separate entities. These functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0052] In view of the shortcomings and deficiencies of the existing technology, this example embodiment provides a transmission system strapdown inertial navigation method based on Lie group / Lie algebra. Figure 1 As shown, the launch system strapdown inertial navigation method based on Lie group / Lie algebra may specifically include the following steps:

[0053] Step S11, constructing a navigation kinematics model corresponding to the aircraft; wherein the navigation kinematics model is used to represent the strapdown inertial navigation model of the aircraft based on the position, velocity, and attitude characteristics of the aircraft in the launch coordinate system;

[0054] Step S12: Based on the Lie group representation of the aircraft motion, a corresponding Lie group differential equation is established for the navigation kinematic model; wherein the Lie group representation corresponding to the aircraft motion utilizes a special Euclidean group to incorporate the aircraft's attitude, velocity, and position characteristics;

[0055] Step S13, obtaining the inertial measurement unit (IMU) parameters corresponding to the current data processing cycle of the aircraft;

[0056] Step S14: discretize the Lie group differential equation, solve the discretized Lie group differential equation using the IMU parameters corresponding to the current data processing cycle, and obtain updated data of the aircraft's attitude, position, and velocity.

[0057] This method is based on the characteristics of Lie group differential manifolds. The IMU output angular increments and velocity increments can be solved by exponential mapping to obtain attitude and velocity information. The algorithm's compensation for coning error and paddling error is the same as the equivalent rotation vector method. The equivalent rotation vector method needs to discard high-order terms, usually only retaining third-order to fourth-order terms. This method can avoid the errors caused by discarding high-order terms.

[0058] Hereinafter, each step of the transmitting system strapdown inertial navigation method based on Lie groups / Lie algebra in this exemplary implementation will be described in more detail with reference to the accompanying drawings and embodiments.

[0059] In step S11, a navigation kinematics model corresponding to the aircraft is constructed; wherein the navigation kinematics model is used to represent the strapdown inertial navigation model of the aircraft based on the position, velocity, and attitude characteristics of the aircraft in the launch coordinate system;

[0060] Exemplarily, constructing a navigation kinematic model corresponding to the aircraft includes:

[0061] Define the launch coordinate system corresponding to the aircraft; where the origin of the launch coordinate system is O gThe launch point is the launch point, with the x-axis pointing in the launch aiming direction in the horizontal plane of the launch point, the y-axis pointing upward perpendicular to the horizontal plane of the launch point, and the z-axis, x-axis, and y-axis forming a right-handed rectangular coordinate system. The launch coordinate system is fixed to the Earth, and the positional relationship between the launch coordinate system and the Earth is determined based on the geographic latitude B0, longitude λ0, altitude h0, and launch azimuth A0 of the launch point.

[0062] A launch inertial coordinate system is defined based on the launch coordinate system; wherein the launch inertial coordinate system coincides with the launch coordinate system at the moment of launch of the aircraft;

[0063] Define the carrier coordinate system corresponding to the aircraft; where the carrier coordinate system origin is at the center of mass of the aircraft, the x-axis coincides with the longitudinal axis of the aircraft, the y-axis is located in the longitudinal symmetry plane of the aircraft and is perpendicular to the x-axis, and the z-axis forms a right-handed rectangular coordinate system with the x-axis and y-axis;

[0064] Configure the corresponding transformation matrix based on the launch inertial coordinate system and the carrier coordinate system

[0065] According to the position, velocity, attitude characteristics and coordinate system transformation matrix of the aircraft in the launch coordinate system Construct the navigation kinematic model corresponding to the aircraft.

[0066] Specifically, we can first establish a kinematic model for the aircraft, agree on the navigation coordinate system and the carrier coordinate system, and establish the motion differential equation. The aircraft-related coordinate systems may include:

[0067] (1) Earth-centered Earth-fixed coordinate system (e system)

[0068] The Earth-centered, Earth-fixed coordinate system, also known as the e-system, has its origin at the center of the Earth, the x-axis in the equatorial plane pointing to the prime meridian, the z-axis for the Earth's rotation axis pointing to the North Pole, and the y-axis in the equatorial plane forming a right-handed rectangular coordinate system with the x-axis and the z-axis.

[0069] (2) Emission coordinate system (g system)

[0070] The launch coordinate system, that is, the g system, the coordinate origin O g The launch point is the launch point. The x-axis points to the launch aiming direction in the horizontal plane of the launch point. The y-axis is perpendicular to the horizontal plane of the launch point and points upward. The z-axis, x-axis, and y-axis form a right-handed rectangular coordinate system. The launch system is fixed to the earth. The geographic latitude B0, longitude λ0, altitude h0, and launch azimuth A0 of the launch point determine the relationship between the launch coordinate system and the earth, as shown in the following example: Figure 2 shown.

[0071] (3) Launch inertial coordinate system (a system)

[0072] The launch inertial coordinate system, or a-frame, coincides with the launch coordinate system at the moment of launch. Due to the Earth's rotation, the launch coordinate system, fixed to the Earth, changes its orientation in inertial space. Both the launch inertial coordinate system and the geocentric inertial coordinate system are inertial coordinate systems, but their origins and axes point in different directions.

[0073] (4) Carrier coordinate system

[0074] The vehicle coordinate system for the aircraft / carrier, or b-frame, has its origin at the center of mass of the aircraft. For example, if the aircraft is a drone or a missile, the x-axis coincides with the longitudinal axis of the missile, the y-axis lies in the longitudinal symmetry plane of the missile and is perpendicular to the x-axis, and the z-axis forms a right-handed rectangular coordinate system with the x- and y-axes.

[0075] (5) Rotation Matrix

[0076] The rotation matrices for rotating α around the x-axis, y-axis, and z-axis are:

[0077]

[0078] (6) Launch coordinate system and launch inertial coordinate system

[0079] The direction cosine matrix between the launch inertial coordinate system and the launch coordinate system is Expressed as:

[0080]

[0081] Let the time interval from the launch instant to the moment in question be t, then the launch coordinate system rotates around the earth's axis ω ie t angle.

[0082] (7) Launch coordinate system and carrier coordinate system

[0083] Transformation matrix from launch coordinate system to carrier coordinate system Expressed as:

[0084]

[0085] Transformation matrix from carrier coordinate system to launch coordinate system Expressed as:

[0086]

[0087] Since the gyroscope and accelerometer data output is relative to the inertial system, at the initial moment, the launch inertial coordinate system and the launch coordinate system are in a state of overlap. When using Lie group / Lie algebra for strapdown solution, the attitude matrix and velocity information are combined into an SE(3) group, and the differential equation of the launch inertial coordinate system can just meet the conditions for forming an SE(3) group. The strapdown inertial navigation differential equation group in the launch coordinate system is shown in Equation (5):

[0088]

[0089] Among them, V g is the velocity in the launch coordinate system, f b is the specific force of the added output value in the carrier coordinate system, g g is the gravity in the launch coordinate system; in, is the angular velocity of the carrier coordinate system relative to the launch coordinate system; is the angular velocity of the Earth's rotation; P g is the position in the launch coordinate system.

[0090] For example, a Lie group representation of the carrier motion may be defined, the posture, velocity, and position may be incorporated into a special Euclidean group, and differential equations of the group variables may be established.

[0091] The above method also includes:

[0092] Based on the attitude characteristics of the aircraft, a special orthogonal group SO(3) is configured, and the corresponding Lie algebra is configured as well as

[0093] According to the special orthogonal group and the speed characteristics of the aircraft, configure the special Euclidean group SE(3); and configure the corresponding Lie algebra

[0094] According to the mapping relationship between Lie group and Lie algebra, combined with the transformation relationship between the launch inertial coordinate system and the carrier coordinate system, the Lie algebra is determined. The exponential mapping relationship between the special orthogonal group SO(3);

[0095] Based on Lie algebra The exponential mapping relationship between the special orthogonal group SO(3) and the special Euclidean group SE(3) is determined. The index mapping relationship between them.

[0096] Specifically, a Lie group is an algebraic structure consisting of sets and operations, where the group operations satisfy the property of continuous differentiability. Lie groups are mathematical objects that possess both the structure of an algebraic group and the properties of a differential manifold. The combination of their smooth manifold properties and continuous group operations gives Lie groups a unique advantage in solving differential equations.

[0097] The navigation attitude is included in the special orthogonal group SO(3), and the special orthogonal group SO(3) and the velocity are combined into the special Euclidean group SE(3) as shown in equations (6) and (7):

[0098]

[0099] in, express; represents a group variable; y g Indicates the launch system speed.

[0100] A Lie algebra consists of a set V, a number field F, and a binary operation [·,·], where the binary operation is also called a Lie bracket and is represented as: [X, Y].

[0101] Based on the above conditions, the Lie algebra corresponding to the special orthogonal group SO(3) Lie algebra corresponding to the special Euclidean group SE(3) The definitions are:

[0102]

[0103] in, φ represents the Lie algebra corresponding to the rotational motion of the rigid body, which is the angular velocity during rotational motion, and its physical meaning is expressed as ω; ρ represents the Lie algebra corresponding to the translational motion of the rigid body, and its physical meaning is the velocity v during translational motion.

[0104] The relationship between Lie groups and Lie algebras can be expressed as Figure 3 To express, Lie algebra T E M (grid plane) is the tangent space of the Lie group manifold M (here represented by a light blue sphere) at the unit point ε. By exponential mapping, every red straight line path ζ from the origin on the Lie algebra i Generates yellow mapping paths exp(ζ along their respective paths around the manifold i ). Every element in a Lie group has a completely equivalent linear vector space in a Lie algebra.

[0105] Among them, the exponential mapping of the matrix is:

[0106]

[0107] Where φ = θa, a^ represents the antisymmetric matrix of the unit vector a, satisfying the following two properties:

[0108] a^a^=aa T -I a^a^a^=-a^ (11)

[0109] Then the direction cosine matrix There is the following conversion relationship with the rotation vector:

[0110]

[0111] Thus we get Exponential mapping to SO(3).

[0112] On this basis, it can be deduced that The exponential mapping is:

[0113]

[0114] Among them, Ω=cosθI+(1-cosθ)aa T +sinθa^.

[0115] In step S12, based on the Lie group representation of the aircraft motion, a corresponding Lie group differential equation is established for the navigation kinematic model; wherein the Lie group representation corresponding to the aircraft motion utilizes a special Euclidean group to incorporate the attitude, velocity and position characteristics of the aircraft.

[0116] Exemplarily, based on the Lie group representation of aircraft motion, a corresponding Lie group differential equation is established for the navigation kinematic model, including:

[0117] Based on the navigation kinematic model of the aircraft, the special Euclidean group SE(3) and Lie algebra s The exponential mapping relationship between e(3) configures the Lie group differential equation: in, is the Lie algebra of the Lie group Y, V=(v;ω) T ∈se(3); v is the velocity, ω is the angular velocity.

[0118] Specifically, Lie groups are continuous groups. Special orthogonal groups and special Euclidean groups are both time-continuous groups and are a type of Lie group. Here we take the attitude transformation of an aircraft as an example. Suppose the attitude rotation matrix of the coordinate system g relative to the reference system a can be expressed as Since the rotation matrix is an orthogonal matrix with determinant 1, satisfying If the condition Pose Matrix The differential equation is:

[0119]

[0120] in, is the angular velocity of system b relative to system g, for The antisymmetric matrix of .

[0121] Formula (14) is a first-order homogeneous differential equation, and its solution can be expressed as:

[0122]

[0123] For the discrete time The increment describes the mapping relationship between angular velocity and attitude transformation matrix, It is the Lie algebra so(3) corresponding to the special orthogonal group SO(3).

[0124] Since φ^ represents a single sampling period The increment of , whose differential is defined as:

[0125]

[0126] According to the BCH (Baker-Campbel-Hausdorff) formula:

[0127]

[0128] It can be solved as follows:

[0129]

[0130] Among them, φ represents the cumulative amount of ω during this period of time, that is,

[0131] Similarly, ρ represents the cumulative amount of v during this period of time, that is,

[0132] In order to facilitate the subsequent formula expression, the following formulas are simply expressed:

[0133]

[0134] Therefore, for a given T∈se(3), the differential of its exponential mapping can be expressed as:

[0135]

[0136] in,

[0137]

[0138] in,

[0139]

[0140] From this we can get the solution method of the differential equation corresponding to the special orthogonal group SO(3). Since the special Euclidean group and the special orthogonal group are similar in form, their solutions are also similar. The differential equation corresponding to the special Euclidean group is:

[0141]

[0142] Among them, Y′ represents the result after updating the solution, V=(v;ω) T ∈se(3), then It is the Lie algebra of the Lie group Y.

[0143] In step S13, the inertial measurement unit (IMU) parameters corresponding to the current data processing cycle of the aircraft are obtained.

[0144] For example, during the inertial navigation process, the aircraft can collect IMU parameters corresponding to the data processing cycle in real time. For example, IMU parameters can be collected once during each data processing cycle. The IMU outputs are the angular velocity and specific force of the aircraft.

[0145] Exemplarily, the current data processing cycle includes a plurality of consecutive sampling points.

[0146] The method further includes: accumulating increments of the IMU parameters of the plurality of sampling points, and configuring the accumulated IMU parameter increments as the IMU parameters corresponding to the current data processing cycle.

[0147] Specifically, during a data processing cycle, multiple IMU parameter acquisitions can be configured, with the same time interval between each sampling. Accordingly, the data increments obtained from each sampling can be accumulated, and the accumulated data is used as the IMU parameter for the current cycle and used for data update.

[0148] In step S14, the Lie group differential equation is discretized and the discretized Lie group differential equation is solved using the IMU parameters corresponding to the current data processing cycle to obtain updated data on the attitude, position, and velocity of the aircraft.

[0149] Exemplarily, the above step S14 may include:

[0150] The discretized Lie group differential equation is updated to obtain the spiral Lie algebra from the carrier coordinate system to the launch coordinate system. The spiral Lie algebra includes the attitude characteristics, velocity characteristics, and position characteristics of the aircraft.

[0151] Based on the spiral Lie algebra, the Lie group variables are updated, the IMU parameters are substituted, and the earth's gravity, angular velocity, and the drag velocity caused by the earth's rotation are compensated to solve the increments of attitude, velocity, and position to complete the data update of the attitude, velocity, and position information in the launch coordinate system.

[0152] Exemplarily, the IMU parameters include: the angular velocity and specific force of the aircraft. The method further includes: determining a velocity parameter corresponding to the specific force, so as to introduce the velocity parameter into the Lie group variable.

[0153] Specifically, we can substitute the above Lie group differential equation into the solution and derive the discretization update formula. The solution of the Lie group differential equation is:

[0154] Y(t)=Y(0)exp(T) (26)

[0155] Here, the Lie algebra is defined as T = [ω v] T ∈se(3).

[0156] φ(t) satisfies the differential equation:

[0157]

[0158] Based on the above formula (19), we can get:

[0159]

[0160] Based on the above formula (21), we can get:

[0161]

[0162] Based on the above results, we can get:

[0163]

[0164] The solution of the differential equation (27) can be obtained by using equation (31), and finally, by discretizing it, the Lie group update shown in equation (26) can be obtained.

[0165] Now mark the time parameters k and k+1, and get the group variable at the time Calculate the group variable at time k+1 The update formula is expressed as:

[0166]

[0167] in, is the SE(3) group at the current moment, is the updated SE(3) group, and the exponential map exp(Φ(ΔT)) is the change of the SE(3) group during the update period.

[0168] The above explains the basic concepts of Lie groups / Lie algebras and the solution method of Lie group differential equations.

[0169] For example, in the real-time navigation process of an aircraft, the navigation solution information is provided by the IMU, and the IMU outputs the angular velocity and specific force of the carrier. Therefore, for the navigation solution of the aircraft, the corresponding Lie algebra can be replaced by the specific force f instead of the rigid body velocity v b .

[0170] The corresponding update formula is expressed as:

[0171]

[0172] in,

[0173]

[0174] The attitude differential equation and velocity differential equation are established as differential equations of special Euclidean group SE(3), which can be expressed as:

[0175]

[0176] in, represents a special Euclidean group,

[0177] By solving the above differential equations, we can obtain the attitude transformation matrix of the carrier coordinate system b relative to the inertial coordinate system a: and the velocity of the carrier coordinate system relative to the inertial coordinate system The parameters can then be transformed into the navigation coordinate system.

[0178] Considering that the information collected by the sensor in navigation is discrete information, the computer cannot directly process the differential equation, so it is necessary to discretize the Lie group differential equation. Among them, the key to solving the Lie group differential equation is to calculate the Lie algebra within the update time interval According to the above formula (27), the Lie algebraic differential equation can be expressed as:

[0179]

[0180] Substitute the above formula (31) into the above formula (36) and use the second-order approximation, that is, D = 0, We can get:

[0181]

[0182] Considering that the data update time is very short, Φ∈se(3) is a small quantity during the update period, so the above formula can be approximately expressed as:

[0183]

[0184] in,

[0185] Formula (38) is integrated within the update period and expressed as:

[0186]

[0187] Wherein, α=(Δv; Δθ) is the angular increment and velocity increment within the update period.

[0188] The angular increment and velocity increment can be measured directly by the gyroscope and accelerometer. If the update time interval contains N samples, the relationship between α and the inertial navigation device output is expressed as:

[0189]

[0190] Where Δv i and Δα i Represents the i-th sampling data of the inertial device within the update cycle. The second term in Equation (39) is caused by the non-commutativity error. Unlike the traditional algorithm that needs to calculate two non-commutativity terms, namely, cone and rowing, the Lie group / Lie algebra algorithm only needs to calculate one. The integral term in Equation (39) is represented by ΔΦ s =(Δη s ;Δφ s ) is expressed as follows. The sub-sampling algorithm uses the sampling values within the update period to update ΔΦ s To approximate, the expression is:

[0191]

[0192] Using the minimum error criterion similar to cone compensation, the same optimization coefficient as the traditional cone algorithm can be derived. For example, the twin sample optimization coefficient is K 12 =2 / 3. After obtaining the spiral Lie algebra ΔΦ within the update time interval through the sub-sampling algorithm, the Lie group can be updated through the exponential mapping, which is expressed as:

[0193]

[0194] By solving the above differential equations and performing gravity compensation on the velocity, we can obtain the attitude transformation matrix of the carrier system b relative to the inertial coordinate system a: and the velocity v in the inertial system a The launch inertial system position update adopts a simplified update algorithm, which is expressed as follows:

[0195]

[0196] The transformation matrix from the launch inertial coordinate system to the launch coordinate system can be obtained by formula (42): Then we have:

[0197]

[0198] According to the posture transformation matrix The information of the three attitude angles can be obtained. Similarly, the velocity vector in the launch coordinate system can be obtained through formula (45), which is expressed as:

[0199]

[0200] Therefore, the position of the inertial system P is obtained by Lie Group strapdown inertial navigation update a , we can get the latitude and longitude of the aircraft relative to the earth (B, λ, h), and also get the position P of the aircraft in the earth-centered fixed system. e , and the position P in the launch system can be obtained g .

[0201] Exemplary, reference Figure 4 、 Figure 5 As shown, the launch system strapdown inertial navigation method based on Lie groups / Lie algebras is used for numerical integration of the inertial navigation system. Navigation attitude, velocity, and position change information are calculated based on inertial device information, and then integrated to obtain the navigation information of the carrier. Specifically, this method includes: 1) establishing a kinematic model. The navigation coordinate system and the carrier coordinate system are defined, and the differential equations of motion are established.

[0202] 2) Lie group representation of carrier motion. A Lie group-based description of the aircraft motion state is established, and the attitude and velocity differential equations in the launch coordinate system are incorporated into the Lie group to construct the carrier motion SE(3) model in the launch coordinate system.

[0203] 3) Establish the Lie group differential equation. According to Equation (25), the angular velocity and specific force within an update period are recorded as a Lie algebra and mapped to the Lie group.

[0204] 4) Derive the discretization update formula. According to equations (36) and (39), the discretization update formula of the Lie group differential equation is given.

[0205] 5) Complete the solution of the differential equation. Update the discretized Lie group differential equation according to Equation (42) and solve the spiral Lie algebra from the carrier system to the launch system. Use the spiral Lie algebra to update the Lie group variables (including attitude, velocity, and position) and substitute the IMU measurement values. Compensate for the Earth's gravity, angular velocity, and the drag velocity caused by the Earth's rotation to complete the incremental solution of attitude, velocity, and position, and complete the numerical update of the attitude, velocity, and position information in the launch system.

[0206] The method provided in the embodiment of the present invention is based on the characteristics of Lie group differential manifolds. The IMU output angular increment and velocity increment can be solved by exponential mapping to obtain attitude and velocity information. The algorithm compensates for coning error and paddling error in the same way as the equivalent rotation vector method. The equivalent rotation vector method needs to discard high-order terms and usually only retains third to fourth order terms. This method can avoid the errors caused by discarding high-order terms.

[0207] It should be noted that the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention and are not intended to be limiting. It is readily understood that the processes illustrated in the above figures do not indicate or limit the temporal order of these processes. Furthermore, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0208] It should be noted that, although several modules or units of the device for action execution are mentioned in the above detailed description, this division is not mandatory. In fact, according to an embodiment of the present invention, the features and functions of two or more modules or units described above can be concretized in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided into multiple modules or units to be concretized.

[0209] Figure 6 A schematic diagram of an electronic device suitable for implementing an embodiment of the present invention is shown.

[0210] It should be noted that Figure 6 The electronic device 1000 shown is only an example and should not limit the functions and scope of use of the embodiments of the present invention.

[0211] For example, the electronic device may be an intelligent electronic device installed on an aircraft and used to navigate the aircraft.

[0212] like Figure 6 As shown, electronic device 1000 includes a central processing unit (CPU) 1001, which can perform various appropriate actions and processes according to the program stored in read-only memory (ROM) 1002 or the program loaded from storage portion 1008 into random access memory (RAM) 1003. Various programs and data required for system operation are also stored in RAM 1003. CPU 1001, ROM 1002 and RAM 1003 are connected to each other via bus 1004. Input / output (I / O) interface 1005 is also connected to bus 1004.

[0213] The following components are connected to the I / O interface 1005: an input section 1006 including a keyboard, a mouse, and the like; an output section 1007 including devices such as a cathode ray tube (CRT), a liquid crystal display (LCD), and a speaker; a storage section 1008 including a hard disk; and a communication section 1009 including a network interface card such as a LAN (Local Area Network) card or a modem. The communication section 1009 performs communication processing via a network such as the Internet. A drive 1010 is also connected to the I / O interface 1005 as needed. Removable media 1011, such as a magnetic disk, an optical disk, a magneto-optical disk, or a semiconductor memory, is installed in the drive 1010 as needed, so that computer programs read therefrom can be installed in the storage section 1008 as needed.

[0214] In particular, according to an embodiment of the present invention, the process described below with reference to the flowchart can be implemented as a computer software program. For example, an embodiment of the present invention includes a computer program product that includes a computer program carried on a storage medium, the computer program containing program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network via the communication section 1009 and / or installed from a removable medium 1011. When the computer program is executed by the central processing unit (CPU) 1001, the various functions defined in the system of the present application are performed.

[0215] It should be noted that the storage medium shown in the embodiments of the present invention can be a computer-readable signal medium or a computer-readable storage medium or any combination of the above. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or component, or any combination of the above. More specific examples of computer-readable storage media can include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM), a flash memory, an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present invention, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, device or device. In the present invention, a computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, which carries computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium may also be any storage medium other than a computer-readable storage medium that can transmit, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. Program code contained on the storage medium may be transmitted using any suitable medium, including but not limited to wireless, wired, or any suitable combination thereof.

[0216] The flowcharts and block diagrams in the accompanying drawings illustrate the possible implementation architecture, functions and operations of the systems, methods and computer program products according to various embodiments of the present invention. In this regard, each box in the flowchart or block diagram can represent a module, program segment, or a part of code, and the above-mentioned module, program segment, or a part of code contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in an order different from that marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram or flowchart, and the combination of boxes in the block diagram or flowchart, can be implemented with a dedicated hardware-based system that performs the specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0217] The units involved in the embodiments of the present invention may be implemented in software or hardware, and the units described may also be provided in a processor. In some cases, the names of these units do not limit the units themselves.

[0218] It should be noted that, as another aspect, the present application also provides a storage medium, which can be included in an electronic device; or it can exist independently without being installed in the electronic device. The above storage medium carries one or more programs, and when the above one or more programs are executed by an electronic device, the electronic device implements the method described in the following embodiments. For example, the electronic device can implement the following Figure 1 The individual steps of the method are shown.

[0219] In one embodiment, the present application provides a computer program product, including a computer program, which implements the steps in the above-mentioned method embodiments when executed by a processor.

[0220] Furthermore, the above-described figures are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention and are not intended to be limiting. It is readily understood that the processes illustrated in the above-described figures do not indicate or limit the temporal order of these processes. Furthermore, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0221] Other embodiments of the present invention will readily occur to those skilled in the art after considering the specification and practicing the invention herein. This application is intended to cover any variations, uses, or adaptations of the present invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The description and examples are to be considered as exemplary only, with the true scope and spirit of the invention being indicated by the claims.

[0222] It should be understood that the present invention is not limited to the exact construction described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof, which is limited only by the appended claims.

Claims

1. A strapdown inertial navigation method for a transmitting system based on Lie groups / Lie algebras, characterized in that: The method comprises: Constructing a navigation kinematic model corresponding to the aircraft; wherein the navigation kinematic model is used to represent the aircraft's strapdown inertial navigation model based on the aircraft's position, velocity, and attitude characteristics in the launch coordinate system; Based on the Lie group representation of aircraft motion, the corresponding Lie group differential equations are established for the navigation kinematic model. The Lie group representation of aircraft motion incorporates the attitude, velocity, and position characteristics of the aircraft using a special Euclidean group. Get the IMU parameters corresponding to the current data processing cycle of the aircraft; The Lie group differential equation is discretized and solved using the IMU parameters corresponding to the current data processing cycle to obtain updated data on the aircraft's attitude, position, and velocity.

2. The method according to claim 1, characterized in that The constructing of a navigation kinematic model corresponding to the aircraft includes: Define the launch coordinate system corresponding to the aircraft; where the origin of the launch coordinate system is O g The launch point is the launch point, with the x-axis pointing in the launch aiming direction in the horizontal plane of the launch point, the y-axis pointing upward perpendicular to the horizontal plane of the launch point, and the z-axis, x-axis, and y-axis forming a right-handed rectangular coordinate system. The launch coordinate system is fixed to the Earth, and the positional relationship between the launch coordinate system and the Earth is determined based on the geographic latitude B0, longitude λ0, altitude h0, and launch azimuth A0 of the launch point. A launch inertial coordinate system is defined based on the launch coordinate system; wherein the launch inertial coordinate system coincides with the launch coordinate system at the moment of launch of the aircraft; Define the carrier coordinate system corresponding to the aircraft; where the carrier coordinate system origin is at the center of mass of the aircraft, the x-axis coincides with the longitudinal axis of the aircraft, the y-axis is located in the longitudinal symmetry plane of the aircraft and is perpendicular to the x-axis, and the z-axis forms a right-handed rectangular coordinate system with the x-axis and y-axis; Configure the corresponding transformation matrix based on the launch inertial coordinate system and the carrier coordinate system According to the position, velocity, attitude characteristics and coordinate system transformation matrix of the aircraft in the launch coordinate system Construct the navigation kinematic model corresponding to the aircraft, including: Among them, V g is the velocity in the launch coordinate system, f b is the specific force of the added output value in the carrier coordinate system, g g is the gravity in the launch coordinate system; in, is the angular velocity of the carrier coordinate system relative to the launch coordinate system; is the angular velocity of the Earth's rotation; P g is the position in the launch coordinate system.

3. The method according to claim 1, characterized in that The method further comprises: Based on the attitude characteristics of the aircraft, a special orthogonal group SO(3) is configured, and the corresponding Lie algebra is configured as well as According to the special orthogonal group and the velocity characteristics of the aircraft, configure the special Euclidean group SE(3); and configure the corresponding Lie algebra According to the mapping relationship between Lie group and Lie algebra, combined with the transformation relationship between the launch inertial coordinate system and the carrier coordinate system, the Lie algebra is determined. The exponential mapping relationship between the special orthogonal group SO(3); Based on Lie algebra The exponential mapping relationship between the special orthogonal group SO(3) and the special Euclidean group SE(3) is determined. The index mapping relationship between them.

4. The method according to claim 3, characterized in that Based on the Lie group representation of aircraft motion, the corresponding Lie group differential equations are established for the navigation kinematic model, including: Based on the navigation kinematic model of the aircraft, combined with the special Euclidean group SE(3) and Lie algebra The exponential mapping relationship between them configures the Lie group differential equation: in, is the Lie algebra of the Lie group Y, V=(v;ω) T ∈se(3); v is the velocity, ω is the angular velocity.

5. The method according to claim 1, wherein Discretizing the Lie group differential equation, solving the discretized Lie group differential equation using the IMU parameters corresponding to the current data processing cycle, and obtaining updated data on the attitude, position, and velocity of the aircraft include: The discretized Lie group differential equation is updated to obtain the spiral Lie algebra from the carrier coordinate system to the launch coordinate system. The spiral Lie algebra includes the attitude characteristics, velocity characteristics, and position characteristics of the aircraft. Based on the spiral Lie algebra, the Lie group variables are updated, the IMU parameters are substituted, and the earth's gravity, angular velocity, and the drag velocity caused by the earth's rotation are compensated to solve the increments of attitude, velocity, and position to complete the data update of the attitude, velocity, and position information in the launch coordinate system.

6. The method according to claim 5, characterized in that The IMU parameters include: angular velocity and specific force of the aircraft; The method further comprises: A velocity parameter corresponding to the specific force is determined, so as to be used for bringing the velocity parameter into the Lie group variable.

7. The method according to claim 1, characterized in that The current data processing cycle includes a plurality of continuous sampling points; The method further comprises: The increments of the IMU parameters of multiple sampling points are accumulated, and the accumulated IMU parameter increments are configured as the IMU parameters corresponding to the current data processing cycle.

8. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the transmitting system strapdown inertial navigation method based on Lie group / Lie algebra is implemented as claimed in any one of claims 1 to 7.

9. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the transmitting system strapdown inertial navigation method based on Lie group / Lie algebra according to any one of claims 1 to 7 is implemented.

10. An electronic device, characterized in that: include: processor; as well as a memory for storing executable instructions of the processor; The processor is configured to execute the transmit-system strapdown inertial navigation method based on Lie groups / Lie algebras according to any one of claims 1 to 7 by executing the executable instructions.

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