A high-precision inertial navigation velocity solution method based on earth-fixed coordinate system

Abstract

The present invention discloses a high-precision inertial navigation velocity solution method based on an earth-fixed coordinate system, comprising: determining a velocity solution equation based on an earth-fixed coordinate system; determining t k The attitude transformation matrix of the body coordinate system relative to the ground-fixed coordinate system at time t k The apparent acceleration of the body coordinate system relative to the ground-fixed coordinate system at the moment; according to the solution equation, the velocity is updated and the velocity is calculated at t k+1 The present invention uses the angular rates output by three gyroscopes orthogonally mounted on the inertial system body and the kinematic equations input from three accelerometers to achieve real-time updates of the inertial navigation attitude angle and acceleration. During the update process, a discretized velocity analytical solution with an explicit expression is used to improve the solution accuracy and ensure the stability of the body coordinate system relative to the Earth-fixed coordinate system. This present invention is the first to provide a method for calculating the discretized velocity analytical solution for an inertial system based on an Earth-fixed coordinate system, with the advantages of high accuracy and fast calculation speed.

Description

Technical Field

[0001] The present application relates to the technical field of aviation and aerospace, and in particular to a high-precision inertial navigation velocity solution method based on an earth-fixed coordinate system. Background Art

[0002] The primary function of inertial navigation is to determine the position, velocity, and attitude of a vehicle relative to a computational coordinate system in real time. Strapdown inertial systems are directly connected to the vehicle, using gyroscopes to measure angular velocity and accelerometers to measure apparent acceleration. These measurements are then mathematically solved to provide attitude and velocity information. Platform-based systems have their inertial components mounted on a physical platform. Gyroscopes are used to stabilize the platform, driven by servo motors, ensuring it remains parallel to a spatial rectangular coordinate system. The sensitive axes of the three accelerometers are aligned with the three axes of this coordinate system to measure the vehicle's apparent acceleration along the three axes.

[0003] At present, the solution method for velocity update generally adopts numerical integration method, such as the fourth-order Runge-Kutta method, the sixth-order and fifth-order England method, etc. However, the disadvantage of numerical integration method is the existence of truncation error. Especially when the velocity changes rapidly, the standard numerical integration solution will have errors. Summary of the Invention

[0004] This application provides a high-precision inertial navigation velocity solution method based on an earth-fixed coordinate system, which aims to reduce the amount of calculation while reducing errors, improving inertial navigation accuracy, and achieving high-precision navigation.

[0005] In a first aspect, a high-precision inertial navigation velocity solution method based on an earth-fixed coordinate system is provided, comprising:

[0006] Determine t k The angular velocity vector of the Earth-fixed coordinate system relative to the inertial coordinate system at time

[0007] According to t k Coordinate transformation matrix from the body coordinate system to the earth-fixed coordinate system at the moment and t k The apparent acceleration of the body coordinate system relative to the inertial coordinate system at the moment Determine t k The apparent acceleration of the body coordinate system relative to the earth-fixed coordinate system at the moment

[0008] According to t k The speed of time and t k The apparent acceleration of the body coordinate system relative to the earth-fixed coordinate system at the moment Find t k+1 =t k The speed at time +ΔT is

[0009]

[0010] ΔT is the time sampling step, t k The normal gravity vector in the Earth-fixed coordinate system at time .

[0011] In conjunction with the first aspect, in certain implementations of the first aspect, the attitude conversion matrix of the body coordinate system relative to the ground-fixed coordinate system at the initial time t0 is:

[0012]

[0013] Where, is the coordinate transformation matrix from the body coordinate system to the geographic coordinate system obtained through initial alignment; is the coordinate transformation matrix from the geographic coordinate system to the earth-fixed coordinate system at the initial moment; λ0 is the longitude at the initial moment; is the latitude at the initial moment.

[0014] In conjunction with the first aspect, in certain implementations of the first aspect, at t k+1 The attitude transformation matrix of the body coordinate system relative to the ground-fixed coordinate system at this moment By t k The angular velocity of the body coordinate system relative to the earth-fixed coordinate system at the moment Calculation yields:

[0015]

[0016] Where I is the identity matrix;

[0017] t k The attitude transformation matrix of the body coordinate system relative to the earth-fixed coordinate system at this moment;

[0018]

[0019] In conjunction with the first aspect, in certain implementations of the first aspect, t k The angular velocity of the body coordinate system relative to the earth-fixed coordinate system at the moment The calculation method is:

[0020]

[0021] Where, t k The drift angular velocity of the body coordinate system relative to the inertial coordinate system at the moment is calculated in real time based on the error coefficient bound in the navigation computer. t k The angular velocity of the Earth relative to the inertial coordinate system at this moment; t k The coordinate transformation matrix of the body relative to the earth-fixed coordinate system at this moment,

[0022] In combination with the first aspect, in certain implementations of the first aspect, when the inertial navigation system is a strapdown type, the velocity update equation and the coordinate transformation matrix update equation of the inertial navigation are applied to the velocity determination of the optical gyro strapdown inertial navigation, or to the velocity determination of the electromechanical gyro strapdown inertial navigation.

[0023] In combination with the first aspect, in certain implementations of the first aspect, when the inertial navigation system is platform-type, the inertial navigation velocity update equation and the coordinate transformation matrix update equation are applied to determine the inertial navigation velocity of the fiber optic platform, or to determine the inertial navigation velocity of the three-floating platform.

[0024] In conjunction with the first aspect, in some implementations of the first aspect, the method further includes:

[0025] According to t k+1 The speed of time Update k+1 The location at the moment.

[0026] In combination with the first aspect, in some implementations of the first aspect, according to t k+1 The speed of time Update k+1 The position at a given moment is calculated as:

[0027]

[0028] Where, t k The position of the carrier in the earth-fixed coordinate system at the moment, t k+1 The position of the carrier in the Earth-fixed coordinate system at this moment.

[0029] In combination with the first aspect, in some implementations of the first aspect, by installing a gyroscope on the inertial system body, t k The three-axis apparent acceleration components of the body coordinate system at the moment and

[0030] In a second aspect, a navigation system is provided, wherein the navigation system is configured to execute the method as described in any one of the implementations of the first aspect.

[0031] Compared with the existing technology, the solution provided by this application includes at least the following beneficial technical effects:

[0032] (1) This invention discloses a high-precision inertial navigation velocity calculation method based on an Earth-fixed coordinate system. Compared to numerical integration methods, this method can directly and accurately calculate the velocity of the body coordinate system relative to the Earth-fixed coordinate system. Traditional numerical solutions calculate the velocity through continuous iteration. When processing large amounts of data, it can quickly generate results, improving processing efficiency.

[0033] (2) The present invention discloses a high-precision inertial navigation velocity solution method based on an earth-fixed coordinate system, and provides a discretized velocity analytical solution with an explicit expression, which effectively reduces the problem of large truncation error caused by discretization when the velocity changes rapidly, and improves the accuracy of the solution.

[0034] (3) The present invention discloses a high-precision inertial navigation velocity calculation method based on an earth-fixed coordinate system. This calculation method can be used for velocity calculation of both strapdown systems and platform systems, and is universal. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a data flow chart of a high-precision inertial navigation velocity calculation method based on an earth-fixed coordinate system in an embodiment of the present invention.

[0036] Figure 2 Schematic diagram of the relationship between the ground-fixed coordinate system and the carrier coordinate system in an embodiment of the present invention.

[0037] Figure 3 The present invention is a schematic diagram of three speeds and positions of an aircraft during three rolls calculated using the analytical solution of the present invention.

[0038] Figure 4 The present invention is a schematic diagram of a three-dimensional trajectory of an aircraft using navigation solution based on the speed calculated by the present invention.

[0039] Figure 5 A schematic diagram of velocity truncation error estimation based on the fourth-order Runge-Kutta method. DETAILED DESCRIPTION

[0040] The present application is described in further detail below with reference to the accompanying drawings and specific embodiments.

[0041] like Figure 1 The present invention provides a high-precision inertial navigation velocity calculation method based on an Earth-fixed coordinate system. This method can be implemented using either a strapdown inertial system fixed to a carrier or a platform-based inertial system. This method accurately discretizes the velocity differential equation of the inertial system, ensuring a precise description of the velocity of the inertial system's body coordinate system relative to the Earth-fixed coordinate system, thereby improving the navigation accuracy of the Earth-fixed inertial system. The specific steps are as follows.

[0042] Step 1: Determine tk The angular velocity of the earth-fixed coordinate system (which can be represented by the subscript e in the formula) relative to the inertial coordinate system (which can be represented by the subscript i in the formula) at the moment is ω ie , the angular velocity vector The antisymmetric matrix in the ground-fixed coordinate system is denoted as The normal gravity vector in the Earth-fixed coordinate system at time tk is expressed as

[0043] In this embodiment, if Figure 2 The body coordinate system corresponding to the inertial system is recorded as O'-X'Y'Z', which is a moving system; among them, the origin O' is the geometric center of the body of the inertial system, the O'X' axis indicates that the horizontal axis of the carrier points to the right, the O'Y' axis indicates that the longitudinal axis of the carrier points forward, and the O'Z' axis, O'X' axis and O'Y' axis form a right-handed coordinate system.

[0044] The Earth-fixed coordinate system is denoted as O-XYZ, which is a fixed system; among them, the origin O is the center of the earth, the OX axis points to the mean Green meridian, the OY axis is perpendicular to the OX and OZ axes, forming a right-handed system, and the OZ axis is parallel to the mean earth's rotation axis.

[0045] Step 2: Determine t during the movement k+1 The attitude transformation matrix of the body coordinate system (which can be represented by the subscript b in the formula) relative to the ground-fixed coordinate system at the moment

[0046] The attitude transformation matrix of the body coordinate system relative to the ground-fixed coordinate system at the initial time t0 is:

[0047]

[0048] Where, is the coordinate transformation matrix from the body coordinate system to the geographic coordinate system obtained through initial alignment; is the coordinate transformation matrix from the geographic coordinate system to the earth-fixed coordinate system at the initial moment; λ0 is the longitude at the initial moment; is the latitude at the initial moment.

[0049] By t k The angular velocity of the body coordinate system relative to the earth-fixed coordinate system at the moment Calculated at t k+1 The attitude transformation matrix of the body coordinate system relative to the ground-fixed coordinate system at this moment

[0050] t k The angular velocity of the body coordinate system relative to the earth-fixed coordinate system at the moment The calculation method is:

[0051]

[0052] Where, t k The angular velocity of the body coordinate system relative to the inertial coordinate system at the moment; when the inertial navigation system is a platform type, t k The drift angular velocity of the body coordinate system relative to the inertial coordinate system at any moment is calculated in real time based on the error coefficient bound in the navigation computer; t k The angular velocity of the Earth relative to the inertial coordinate system at this moment; t k The coordinate transformation matrix of the body relative to the earth-fixed coordinate system at this moment,

[0053] Calculated by the following formula

[0054]

[0055] Where I is the identity matrix. t k The attitude transformation matrix of the body coordinate system relative to the ground-fixed coordinate system at the moment. ΔT is the sampling step at the moment, that is, ΔT = t k+1 -t k .

[0056] Step 3: Determine t k The apparent acceleration of the body coordinate system relative to the earth-fixed coordinate system at the moment

[0057] The gyroscope is installed on the inertial system body. During the movement, is the accelerometer at t k The apparent acceleration output at each moment, and t k The three-axis apparent acceleration components of the body coordinate system at the moment. is the coordinate transformation matrix from the body coordinate system to the earth-fixed coordinate system.

[0058] Step 4, according to t k The speed of time We can obtain t k+1 =t k The speed at time +ΔT is

[0059]

[0060] Step 5, according to t k+1 The speed of time Update k+1 The position at the moment. The position is calculated as:

[0061]

[0062] Where, t k The position of the carrier in the earth-fixed coordinate system at the moment, t k+1 The position of the carrier in the Earth-fixed coordinate system at this moment.

[0063] In the above-mentioned high-precision inertial navigation velocity solution method based on the earth-fixed coordinate system, the velocity update equation and coordinate transformation matrix update equation of the strapdown inertial navigation can be applied to the velocity determination of the optical gyro strapdown inertial navigation, and can also be applied to the velocity determination of the electromechanical gyro strapdown inertial navigation.

[0064] In the above-mentioned high-precision inertial navigation velocity solution method based on the ground-fixed coordinate system, the velocity update equation and coordinate transformation matrix update equation of the platform-type inertial navigation can be applied to the determination of the inertial navigation velocity of the fiber-optic platform, and can also be applied to the determination of the inertial navigation velocity of the three-floating platform.

[0065] Based on the above embodiments, a group of examples are used for comparison to illustrate the present invention.

[0066] When the strapdown inertial navigation is used to calculate the speed of an aircraft during a certain movement, the speed and position of 1700s to 2700s calculated by the method of the present invention are as follows: Figure 3 As shown, Figure 3 a, 3b, 3c, 3d, 3e, and 3f are the eastward speed v e , northward speed v n , celestial velocity v u (unit is "m / s") and position coordinates X, Y, Z (unit is "m"); Based on the speed of 1700s to 2700s calculated by the method of the present invention, the three-dimensional trajectory of the aircraft motion calculated by navigation is as follows Figure 4 , the position error is less than 20m. It can be seen that the present invention can well reproduce the movement process of the aircraft with large attitude and high maneuverability.

[0067] If only the following fourth-order Runge-Kutta method is used for iterative solution:

[0068]

[0069] Local truncation error estimation of the fourth-order Runge-Kutta method using the sixth-order fifth-order England method

[0070]

[0071] but

[0072] The speed error from 1700s to 2700s is as follows: Figure 5 As shown, Figure 5 a, 5b, 5c are the eastward velocity errors dv e , north velocity error dv n , celestial velocity error dv u (Unit is "m / s"). Figure 5 It can be seen that around 2150s, the eastward velocity error is close to -2.6m / s, the northward velocity error is close to 2.3m / s, and the celestial velocity error is close to 1.8m / s. When the vehicle speed is fast and changes rapidly, the error caused cannot be ignored.

[0073] The above embodiments can verify the correctness of the high-precision inertial navigation velocity solution method based on the earth-fixed coordinate system described in the present invention, which is conducive to achieving high-precision velocity and position solution.

[0074] In summary, the present invention uses a strapdown inertial navigation system (SINS) as an example, using the angular rate outputs of three gyroscopes and the apparent acceleration outputs of three accelerometers orthogonally mounted on the SINS body as input information for the velocity update equation based on an Earth-fixed coordinate system to achieve real-time updates of the inertial navigation attitude angle and acceleration. During the velocity update process, a method for providing an analytical solution to the velocity improves the solution accuracy and ensures the stability of the body coordinate system relative to the Earth-fixed coordinate system. This invention, for the first time, provides a method for analytically solving the discretized velocity of an inertial system based on an Earth-fixed coordinate system, offering the advantage of high accuracy.

[0075] Although the present invention is disclosed above in terms of preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention shall be based on the scope defined by the claims of the present invention.

Claims

1. A high-precision inertial navigation velocity solution method based on an earth-fixed coordinate system, characterized in that: include: Determine t k The angular velocity vector of the Earth-fixed coordinate system relative to the inertial coordinate system at time According to t k Coordinate transformation matrix from the body coordinate system to the earth-fixed coordinate system at the moment and t k The apparent acceleration of the body coordinate system relative to the inertial coordinate system at the moment Determine t k The apparent acceleration of the body coordinate system relative to the earth-fixed coordinate system at the moment According to t k The speed of time and t k The apparent acceleration of the body coordinate system relative to the earth-fixed coordinate system at the moment Find t k+1 =t k The speed at time +ΔT is ΔT is the time sampling step, t k The normal gravity vector in the Earth-fixed coordinate system at time .

2. The method according to claim 1, characterized in that The attitude transformation matrix of the body coordinate system relative to the ground-fixed coordinate system at the initial time t0 is: Where, is the coordinate transformation matrix from the body coordinate system to the geographic coordinate system obtained through initial alignment; is the coordinate transformation matrix from the geographic coordinate system to the earth-fixed coordinate system at the initial moment; λ0 is the longitude at the initial moment; is the latitude at the initial moment.

3. The method according to claim 1, characterized in that In t k+1 The attitude transformation matrix of the body coordinate system relative to the ground-fixed coordinate system at this moment By t k The angular velocity of the body coordinate system relative to the earth-fixed coordinate system at the moment Calculation yields: Where I is the identity matrix; t k The attitude transformation matrix of the body coordinate system relative to the earth-fixed coordinate system at this moment; 4. The method according to claim 3, characterized in that t k The angular velocity of the body coordinate system relative to the earth-fixed coordinate system at the moment The calculation method is: Where, t k The angular velocity of the body coordinate system relative to the inertial coordinate system at the moment, t k The angular velocity of the Earth relative to the inertial coordinate system at this moment; t k The coordinate transformation matrix of the body relative to the earth-fixed coordinate system at this moment, 5. The method according to claim 4, characterized in that When the inertial navigation system is a strapdown type, the velocity update equation and the coordinate transformation matrix update equation of the inertial navigation are applied to the velocity determination of the optical gyro strapdown inertial navigation or to the velocity determination of the electromechanical gyro strapdown inertial navigation.

6. The method according to claim 4, characterized in that When the inertial navigation system is a platform type, the inertial navigation speed update equation and the coordinate transformation matrix update equation are applied to determine the inertial navigation speed of the fiber optic platform, or applied to determine the inertial navigation speed of the three-floating platform.

7. The method according to claim 1, characterized in that The method further comprises: According to t k+1 The speed of time Update k+1 The location at the moment.

8. The method according to claim 7, characterized in that According to t k+1 The speed of time Update k+1 The position at a given moment is calculated as: Where, t k The position of the carrier in the earth-fixed coordinate system at the moment, t k+1 The position of the carrier in the Earth-fixed coordinate system at this moment.

9. The method according to claim 1, characterized in that By installing the gyroscope on the inertial system body, t k The three-axis apparent acceleration components of the body coordinate system at the moment and 10. A navigation system, characterized in that: The navigation system is configured to execute the method according to any one of claims 1 to 9 .

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