Lie group strapdown inertial navigation error model based on carrier system quaternion attitude error

Abstract

The application relates to a Lie group strapdown inertial navigation error model based on a carrier system quaternion attitude error, which comprises that the quaternion attitude error can be divided into a navigation system quaternion attitude error and a carrier system quaternion attitude error, the application first deduces an attitude error model based on the carrier system quaternion, then on the basis, a Lie group strapdown inertial navigation error model based on the carrier system quaternion attitude error is proposed and deduced, the model has obvious advantages in the aspects of combined navigation positioning precision, error convergence speed and filter robustness, and the advantages are more prominent especially under the condition of large misalignment angle. Through experiment comparison of the advantages and disadvantages of four models, the application improves the deficiency of the existing literature on the combined navigation model under the condition of large misalignment angle, and the model can complete high-precision nonlinear combined navigation in a short time under the condition of large misalignment, and meets the requirement of high-precision combined navigation.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of navigation technology, and particularly relates to a Lie group strapdown inertial navigation error estimation method based on a carrier system quaternion attitude error. BACKGROUND

[0002] The strapdown inertial navigation system mainly completes navigation by measuring the specific force of the carrier in the axial direction, and the positioning principle is very simple. According to the Newtonian principle of inertia, the specific force and acceleration of the carrier are measured by using inertial devices (gyroscopes and accelerometers), and the attitude, speed and position information of the carrier can be obtained through integration and various algorithms. For the strapdown inertial navigation system, the inertial measurement unit (IMU) is directly connected with the carrier, so the output of the IMU is the angular velocity and acceleration of the carrier relative to the inertial space, and the acceleration data measured in the carrier coordinate system is converted to the navigation coordinate system for calculation by the navigation computer. The strapdown inertial navigation system uses a digital platform realized by a computer to replace the physical platform, has high reliability, small size and low price, and gradually becomes the main form of the inertial navigation system and is widely used in the fields of aviation, aerospace, navigation and other fields.

[0003] The inertial navigation system is an autonomous navigation system, is not affected by external interference, has complete information, has very good short-term accuracy and stability. However, any precision instrument, no matter how cleverly designed and improved, inevitably has various errors. The errors of the inertial navigation system will accumulate with time, and the long-distance and high-precision navigation is limited. Therefore, other navigation systems such as the global satellite navigation system and the Doppler log navigation are generally used to assist the inertial navigation to constitute a combined navigation system, so as to realize high-precision, long-time, continuous, real-time and high-reliability combined navigation positioning.

[0004] Before combined navigation is performed, initial alignment must be performed to obtain accurate attitude, speed and position information. The speed and position can be easily obtained by the satellite navigation system, and the difficulty lies in the alignment of the attitude information. Generally, accurate initial alignment is performed to make the initial attitude error angle reach a very small value. However, in actual application, an important problem needs to be considered - the misalignment angle is a large misalignment angle. Since the misalignment angle is a large misalignment angle, the small angular velocity approximation cannot be performed, and the system is nonlinear. Therefore, the combined navigation based on the large misalignment angle is becoming a hot spot of research by scholars, and the related research is relatively active.

[0005] General attitude error definition considers that the attitude error exists between the navigation coordinate system (n system) and the calculated navigation coordinate system (n system), and considers that the carrier coordinate system (b system) and the calculated carrier coordinate system (b system) are almost coincident. In fact, from the perspective of Lie group, the attitude error model based on the carrier system is superior to the attitude error model based on the navigation system. In terms of the representation of the attitude, the quaternion is obviously superior to the Euler angle. Therefore, the present application mainly focuses on the Lie group strapdown inertial navigation error model based on the carrier system quaternion attitude error, which is more obvious and outstanding in performance than the Lie group strapdown inertial navigation error model based on the navigation system quaternion, the Lie group strapdown inertial navigation error model based on the navigation system Euler angle and the Lie group strapdown inertial navigation error model based on the carrier system Euler angle. SUMMARY

[0006] In view of the above problems, the present application aims to provide a Lie group strapdown inertial navigation error model based on the carrier system quaternion attitude error, which aims to realize high-precision rapid startup of the carrier under the condition of large misalignment angle, so as to improve the insufficient research on the combined navigation model under the condition of large misalignment angle in the existing literature. The model can complete high-precision nonlinear combined navigation in a short time under the condition of large misalignment, and meet the requirements of high-precision combined navigation.

[0007] A Lie group strapdown inertial navigation error model based on the carrier system quaternion attitude error, comprising: first deriving the attitude error based on the carrier system quaternion, then proposing the Lie group strapdown inertial navigation error model based on the carrier system quaternion attitude error, then comparing the Lie group strapdown inertial navigation error model based on the navigation system quaternion attitude error, the Lie group strapdown inertial navigation error model based on the navigation system Euler angle and the Lie group strapdown inertial navigation error model based on the carrier system Euler angle, and comparing the advantages and disadvantages of the four models through experiments, the specific steps comprising:

[0008] 1) analyzing the definition of the quaternion attitude error, mainly divided into two kinds of navigation system quaternion attitude error and carrier system quaternion attitude error;

[0009] 2) based on the definition of the carrier system quaternion attitude error, deriving the quaternion attitude error model based on the carrier system;

[0010] 3) based on the carrier system quaternion attitude error model, deriving the Lie group strapdown inertial navigation error model based on the carrier system quaternion;

[0011] 4) comparing and analyzing the Lie group strapdown inertial navigation error model based on the carrier system quaternion attitude error with the strapdown inertial navigation error model based on the navigation system quaternion attitude error, the Lie group strapdown inertial navigation error model based on the navigation system Euler angle and the Lie group strapdown inertial navigation error model based on the carrier system Euler angle;

[0012] 5) Through the vehicle-mounted combined navigation experiment, the performance of the Lie group strapdown inertial navigation error model based on the body system quaternion attitude error, the strapdown inertial navigation error model based on the navigation system quaternion attitude error, the Lie group strapdown inertial navigation error model based on the navigation system Euler angle and the Lie group strapdown inertial navigation error model based on the body system Euler angle is compared.

[0013] The application is mainly aimed at the high-precision emergency starting scene of a ship under a large misalignment angle condition, the definition of the attitude error is started, the attitude error model based on the body system quaternion is derived, then the attitude error model is combined with the Lie group strapdown inertial navigation error model to derive the Lie group strapdown inertial navigation error model based on the body system quaternion, finally, through the vehicle-mounted experiment, it is concluded that the performance of the Lie group strapdown inertial navigation error model based on the body system quaternion attitude error is superior to the strapdown inertial navigation error model based on the navigation system quaternion attitude error, the Lie group strapdown inertial navigation error model based on the navigation system Euler angle and the Lie group strapdown inertial navigation error model based on the body system Euler angle, especially the performance advantage of the Lie group strapdown inertial navigation error model based on the body system quaternion is more obvious under the large misalignment angle condition. The application has extremely important significance for the emergency starting of the ship under the large misalignment condition and has strong research value. Respectively, the Lie group strapdown inertial navigation error model based on the navigation system Euler angle, the Lie group strapdown inertial navigation error model based on the body system Euler angle, the Lie group strapdown inertial navigation error model based on the navigation system quaternion and the Lie group strapdown inertial navigation error model based on the body system quaternion are represented. BRIEF DESCRIPTION OF DRAWINGS

[0014] The specific embodiments of the application are further described in detail below with reference to the accompanying drawings.

[0015] Figure 1 The principle block diagram of the four error models involved in the application is shown in the figure;

[0016] Figure 2 The vehicle-mounted experiment trajectory involved in the application is shown in the figure;

[0017] Figure 3 The pitch angle error curve obtained by the Lie group strapdown inertial navigation error model based on the navigation system Euler angle involved in the embodiment of the application is shown in the figure;

[0018] Figure 4 The roll angle error curve obtained by the Lie group strapdown inertial navigation error model based on the navigation system Euler angle involved in the embodiment of the application is shown in the figure;

[0019] Figure 5 The heading angle error curve obtained by the Lie group strapdown inertial navigation error model based on the navigation system Euler angle involved in the embodiment of the application is shown in the figure;

[0020] Figure 6A pitch angle error curve diagram obtained by a Lie group strapdown inertial navigation error model based on a carrier system Euler angle involved in the embodiment of the present application;

[0021] Figure 7 A roll angle error curve diagram obtained by a Lie group strapdown inertial navigation error model based on a carrier system Euler angle involved in the embodiment of the present application;

[0022] Figure 8 A heading angle error curve diagram obtained by a Lie group strapdown inertial navigation error model based on a carrier system Euler angle involved in the embodiment of the present application;

[0023] Figure 9 A pitch angle error curve diagram obtained by a Lie group strapdown inertial navigation error model based on a navigation system quaternion involved in the embodiment of the present application;

[0024] Figure 10 A roll angle error curve diagram obtained by a Lie group strapdown inertial navigation error model based on a navigation system quaternion involved in the embodiment of the present application;

[0025] Figure 11 A heading angle error curve diagram obtained by a Lie group strapdown inertial navigation error model based on a navigation system quaternion involved in the embodiment of the present application;

[0026] Figure 12 A pitch angle error curve diagram obtained by a Lie group strapdown inertial navigation error model based on a carrier system quaternion involved in the embodiment of the present application;

[0027] Figure 13 A roll angle error curve diagram obtained by a Lie group strapdown inertial navigation error model based on a carrier system quaternion involved in the embodiment of the present application;

[0028] Figure 14 A heading angle error curve diagram obtained by a Lie group strapdown inertial navigation error model based on a carrier system quaternion involved in the embodiment of the present application. DETAILED DESCRIPTION

[0029] In order to make the objects and advantages of the present application clearer, the present application will be further described below in conjunction with embodiments. It should be understood that the specific embodiments described herein merely serve to explain the present application and do not limit the present application.

[0030] The preferred embodiments of the present application will be described below with reference to the accompanying drawings. It should be understood by those skilled in the art that the embodiments merely serve to explain the technical principles of the present application and do not limit the protection scope of the present application.

[0031] Reference Figures 1 to 5As shown, the present application relates to a Lie group strapdown inertial navigation error model based on carrier system quaternion attitude error, in order to explain the Lie group strapdown inertial navigation error model based on carrier system quaternion attitude error proposed by the present application in detail, first, the attitude error equation of the carrier system quaternion is given as follows:

[0032]

[0033] The superscript b in the formula represents the carrier coordinate system; the physical meaning of the related quantity is as follows:

[0034] Cnb represents the direction cosine matrix from the b' system to the n system, Cnb represents the carrier system attitude error in the form of direction cosine matrix, Cnb represents the carrier system attitude in the form of quaternion, and I3 represents a three-dimensional matrix in three dimensions, which is an antisymmetric matrix;

[0035] ωb represents the carrier angular velocity information of the b system relative to the inertial coordinate system (i system) output by the gyroscope, ωb represents the carrier angular velocity information with error actually output by the gyroscope, ωnb represents the rotation angular velocity information of the n system relative to the i system, which is composed of two parts: the navigation system conversion caused by the earth rotation and the n system rotation caused by the earth surface bending when the inertial system moves near the earth surface.

[0036] ωb represents the gyroscope measurement error, which can be roughly regarded as the constant drift of the gyroscope, ωb represents the calculation angular velocity error;

[0037] If the attitude and the speed are simultaneously included in a group, a new state quantity ω can be constructed

[0038]

[0039] Then the new error state quantity ω can be obtained

[0040]

[0041] Among them,

[0042] The attitude error equation based on the carrier system quaternion and the Lie group strapdown inertial navigation error equation are combined, and the Lie group strapdown inertial navigation error equation based on the carrier system quaternion is obtained, which is as follows:

[0043] The new state quantity is:

[0044] The new error quantity is:

[0045] Among them, is a newly defined attitude error, is a newly defined velocity error.

[0046] The attitude error direction cosine matrix form and the quaternion form have the following conversion relationship:

[0047]

[0048] The attitude is expressed in the form of quaternion.

[0049] The above is the Lie group strapdown inertial navigation error equation based on the carrier system quaternion, the Lie group strapdown inertial navigation error equation based on the navigation system quaternion, the Lie group strapdown inertial navigation error equation based on the carrier system Euler angle and the Lie group strapdown inertial navigation error equation based on the navigation system Euler angle respectively as follows:

[0050] The Lie group strapdown inertial navigation error equation based on the navigation system quaternion is:

[0051]

[0052] The Lie group strapdown inertial navigation error equation based on the carrier system Euler angle is:

[0053]

[0054] The Lie group strapdown inertial navigation error equation based on the navigation system Euler angle is:

[0055]

[0056] In the above formula, dv n and δp are the conventional definitions of velocity and position error, is the misalignment angle error, τ v is a newly defined velocity error, and has the following relationship:

[0057]

[0058]

[0059] In the formula, R M , R N are the earth meridian radius and the earth colure radius respectively.

[0060] The experimental verification method of the application specifically comprises the following steps:

[0061] (1) The Lie group strapdown inertial navigation error equation based on the navigation system Euler angle is marked as LieEuler-nn,

[0062] The Lie group strapdown inertial navigation error equation based on the carrier system Euler angle is marked as LieEuler-bb,

[0063] The Lie group strapdown inertial navigation error equation based on the navigation system quaternion is marked as LieQuat-nn,

[0064] The Lie group strapdown inertial navigation error equation based on the body system quaternion is marked as LieQuat-bb,

[0065] The state quantity selection of the four equations is specifically represented as:

[0066] LieEuler-nn:

[0067] LieEuler-bb:

[0068] LieQuat-nn:

[0069] LieQuat-bb:

[0070] In the formula, ε b is a constant drift of the gyroscope, is a constant zero offset of the acceleration.

[0071] (2) For the selection of the observation quantity, the velocity and the position are taken as the observation quantity of the integrated navigation:

[0072]

[0073] In the formula, is the velocity and position information obtained by the inertial navigation, and z GPS is the velocity and position reference information obtained by the satellite navigation.

[0074] For the filtering method of the integrated navigation, the Lie group strapdown inertial navigation error model based on the Euler angle adopts the classical Kalman filtering, and the Lie group strapdown inertial navigation error model based on the quaternion adopts the USQUE filtering.

[0075] 3) The vehicle integrated navigation experiment is carried out, and the performances of the four Lie group strapdown inertial navigation error models are analyzed and compared. There is a MEMS inside the vehicle for measuring the sensor output information of the gyroscope and the acceleration, and there is a GPS antenna on the roof for receiving the satellite signal. The velocity error of the GPS is 0.1 m / s, and the position error is 10 m. In addition, there is a high-precision inertial-grade optical fiber inertial navigation inside the vehicle, which can output high-precision attitude information as an attitude reference benchmark. The experiment is about 3000 s in total and is carried out on an open road. The trajectory is shown in Figure 2 The performance indicators of the MEMS are shown in Table 1

[0076]

[0077] The combined navigation system adopts GPS speed and position as observation, and signals can be well received during the whole experiment process.

[0078] Since the error model involved in the application is mainly applied to large misalignment angles, the initial misalignment angle is set to [10° 10° 30°], and the initial speed error and the initial position error are set according to the empirical value, that is, the initial speed error and the initial position error are set to 1 m / s and 10 m respectively.

[0079] Under the above initial conditions, the performances of the four models are compared through the combined navigation experiment based on the vehicle-mounted experimental data. Since GPS can obtain relatively accurate speed and position, but it is difficult to accurately estimate the attitude, the experiment focuses on the estimation of the attitude. Figures 3-5 The estimation errors of the pitch angle, the roll angle and the heading angle respectively. As can be seen from the figure, since the experiment is carried out on a relatively flat road, the pitch angle and the roll angle errors of the four models are small and have little difference, while the estimation error of the heading angle has a large difference. Figure 5 As shown in the figure, under the condition of large misalignment angle, the convergence speed of the LieQuat-bb model is the fastest, and the heading angle error has been reduced to below 1 degree at about 300 s, and the error has been declining and is the smallest thereafter, showing the best performance. The LieEuler-bb model shows the second, and the convergence speed is also fast, and the error converges to below 1 degree at about 400 s, and also remains below 1 degree thereafter, showing a relatively stable state, but the error is always slightly larger than that of the LieQuat-bb model. The LieEuler-nn model and the LieQuat-nn model are relatively similar, although they can also converge to below 1 degree, but it takes a long time.

[0080] From the above analysis, it can be seen that the LieQuat-bb model has the fastest convergence speed, the smallest and most stable attitude estimation error, and is the best in the four Lie group SINS error models, fully showing the fast, stable and high-precision advantages of the proposed model in the application of emergency start under the condition of large misalignment angle.

[0081] So far, the technical solutions of the application have been described in combination with the preferred embodiments shown in the drawings, but those skilled in the art can easily understand that the protection scope of the application is obviously not limited to these specific embodiments. Those skilled in the art can make equivalent changes or replacements to the related technical features without departing from the principles of the application, and the technical solutions after the changes or replacements will fall within the protection scope of the application.

Claims

1. A Lie group strapdown inertial navigation error estimation method based on quaternion attitude error of the carrier system, applied to high-precision rapid start-up under large misalignment angle conditions, characterized in that: I. The attitude error equation for the quaternion of the load system is given as follows: superscript in the formula Indicates the carrier coordinate system. Indicates by The direction cosine matrix from the n-system to the n-system. The attitude error of the carrier system is expressed in the form of a direction cosine matrix. Represents the attitude of the carrier system in quaternion form. This represents a 3D matrix, which is an antisymmetric matrix; For gyroscope output b The frame relative to the inertial coordinate system i The angular velocity information of the carrier system. for The actual angular velocity information of the carrier output by the gyroscope, which contains errors. Represents the rotation of the n-frame relative to the i-frame. Angular velocity information consists of two parts: the navigation frame conversion caused by the Earth's rotation and the rotation of the inertial system near the Earth's surface caused by the curvature of the Earth's surface. This is due to gyroscope measurement error. To calculate the angular velocity error; If both attitude and velocity are included in a group, a new state variable can be constructed: Then we can obtain the new error state quantity: in, For the newly defined attitude error, For the newly defined speed error; The following transformation relationship exists between the cosine matrix form and the quaternion form of the attitude error direction: Represent the attitude using quaternions; II. The error equations of Lie group strapdown inertial navigation based on navigation frame quaternions, Lie group strapdown inertial navigation based on carrier system Euler angles, and Lie group strapdown inertial navigation based on navigation frame Euler angles are as follows: 1) Lie group strapdown inertial navigation error equations based on navigation system quaternions: 2) Lie group strapdown inertial navigation error equations based on Euler angles of the carrier system: 3) Lie group strapdown inertial navigation error equations based on Euler angles of the navigation frame: In the above formula, and δ p represents the conventionally defined velocity and position errors, φ represents the misalignment angle error, and τ represents the misalignment angle error. v Let the newly defined speed error be given, and the following relationship applies: In the formula, Let the radius of the Earth's meridian and the radius of the Earth's zonal circle be denoted respectively. Here, the Lie group strapdown inertial navigation error equation based on the Euler angles of the navigation system is denoted as LieEuler-nn, and the Lie group strapdown inertial navigation error equation based on the Euler angles of the carrier system is denoted as LieEuler-bb. The Lie group strapdown inertial navigation error equation based on navigation system quaternions is denoted as LieQuat-nn. The error equations of Lie group strapdown inertial navigation based on the quaternions of the carrier system are denoted as LieQuat-bb. The specific selection of the state variables for these four equations is as follows: In the formula, For gyroscope constant drift, The acceleration is constant with zero bias; for the selection of observations, velocity and position are used as observations in the integrated navigation system. In the formula, The velocity and position information are obtained from the inertial navigation system. The speed and position reference information is obtained from satellite navigation.

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