CN115855038A - Short-time high-precision attitude keeping method - Google Patents
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Abstract
The invention discloses a short-time high-precision attitude keeping method, which comprises the following steps: acquiring gyroscope output and accelerometer output; obtaining self initial attitude information based on accelerometer output and local gravity acceleration; obtaining a course angle based on the self initial attitude information and the gyroscope output, and outputting the course angle as course output; and obtaining a pitch angle and a yaw angle based on the accelerometer output and the local gravity acceleration, performing low-pass filtering processing, and outputting the pitch angle and the yaw angle after the low-pass filtering processing as horizontal postures to realize posture measurement. The method can rapidly complete the determination of the initial attitude without depending on any external information, does not need to receive any external information during the subsequent attitude measurement, and has strong anti-interference capability. After the violent angular motion, the high-precision attitude measurement can be realized, the accuracy of attitude calculation is improved, and the high-precision attitude measurement under the condition of lower cost is realized.
Description
Technical Field
The invention relates to the field of inertial systems and inertial measurement, in particular to a short-time high-precision attitude keeping method.
Background
The strapdown inertial navigation is a key navigation device of a combat aircraft, the initial alignment precision and speed of the strapdown inertial navigation determine the preparation time of the combat aircraft before takeoff, and the existing inertial navigation self-alignment method generally has the problem of long time and is not beneficial to the quick start of a fighter plane. Therefore, people begin to adopt high-precision laser ranging auxiliary equipment to combine an airborne mark point and an external reference source to quickly measure the heading of the fighter. In the process, the attitude precision of the laser ranging auxiliary equipment is related to the accuracy of the warplane course calculation. In consideration of the non-moving characteristic of the laser ranging auxiliary equipment during working, the method is different from the existing strapdown inertial navigation system, a new attitude reference method is developed, and high-precision attitude measurement under the condition of lower cost is realized.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a short-time high-precision attitude keeping method, which can still realize high-precision attitude measurement after severe angular motion, improve the accuracy of attitude calculation and realize high-precision attitude measurement under the condition of lower cost.
In order to achieve the technical object, the invention provides a short-time high-precision attitude keeping method, which comprises the following steps:
acquiring gyroscope output and accelerometer output;
obtaining self initial attitude information based on the accelerometer output and the local gravity acceleration;
obtaining a course angle based on the self initial attitude information and the gyroscope output, and outputting the course angle as a course;
and obtaining a pitch angle and a yaw angle based on the accelerometer output and the local gravitational acceleration, performing low-pass filtering on the pitch angle and the yaw angle, and outputting the pitch angle and the yaw angle after the low-pass filtering as a horizontal posture so as to realize posture measurement.
Optionally, the gyroscope output is:
wherein, b is a carrier coordinate system; i is an inertial coordinate system;
and &>
Gyroscope angular velocity outputs for the X-axis, Y-axis, and Z-axis, respectively, with T being the transpose.
Optionally, the accelerometer output is:
wherein,
and &>
Accelerometer ratios for the X, Y and Z axes, respectivelyAnd (6) outputting force.
Optionally, the process of acquiring the self initial posture information is as follows:
calculating the projection of the navigation inertial system of the vector of the local gravity acceleration at the initial moment;
calculating the projection of the specific force output by the accelerometer on the carrier inertia system at the initial moment;
and obtaining the self initial attitude information by adopting a double-vector attitude determination method based on the projection of the local gravity acceleration vector in a navigation inertial system at the initial moment and the projection of the specific force output by the accelerometer in a carrier inertial system at the initial moment.
Optionally, the course angle obtaining process includes:
constructing a quaternion differential equation based on the self initial attitude information and the gyroscope output;
and solving by adopting a fourth-order Runge-Kutta method based on the quaternion differential equation to obtain the course angle.
Optionally, the quaternion differential equation is:
in the formula,
is the derivative of the attitude quaternion; w is a four-dimensional antisymmetric array operation associated with a quaternion operation; />
The projection of the strapdown inertial navigation relative to the rotation angular velocity of a navigation coordinate system under a carrier coordinate system is realized; q is an attitude quaternion.
Optionally, the calculation formula of the fourth-order longge-kutta method is:
in the formula, t k Represents a sampling instant; h represents a sampling interval; k is a radical of formula 1 -k 4 The average slope of the quaternion differential equation at different times.
Optionally, the parameters of the low-pass filtering process are set as: the passband cut-off frequency is 1HZ, the stopband cut-off frequency is 10HZ, the passband gain is 1dB, and the stopband gain is-80 dB.
Optionally, the pitch angle and the yaw angle are:
in the formula, theta is a pitch angle; gamma is a roll angle;
and &>
Respectively outputting accelerometer after low-pass filtering treatment of an X axis, a Y axis and a Z axis; g is the local gravitational acceleration.
The invention has the following technical effects:
the method can quickly complete the determination of the initial attitude without depending on any external information, does not need to receive any external information during subsequent attitude measurement, and has strong anti-interference capability. After the violent angular motion, the high-precision attitude measurement can be realized, the accuracy of attitude calculation is improved, and the high-precision attitude measurement under the condition of lower cost is realized.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
Fig. 1 is a flow chart of a short-time high-precision attitude keeping method according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, the invention discloses a short-time high-precision posture maintaining method, which comprises the following steps:
acquiring gyroscope output and accelerometer output;
the gyroscope output is:
the accelerometer output is
Where b denotes the carrier coordinate system and i denotes the inertial coordinate system. />
And &>
Gyroscope angular velocity outputs representing the X-axis, Y-axis, and Z-axis, respectively; />
And &>
Representing specific force output of the accelerometer in the X, Y and Z axes, respectively.
Entering an initial alignment stage to obtain self initial attitude information based on accelerometer output and local gravity acceleration;
two inertial coordinate systems are first defined: (1) Initial moment carrier inertia system b 0 : the coordinate system of the carrier (system b) is coincident with the coordinate system of the carrier at the initial alignment starting time, and is kept still relative to the inertial space. (2) Initial time navigation inertial system n 0 : coinciding with the navigational coordinate system (n-system) at the start of the initial alignment, and remaining stationary with respect to the inertial space. The purpose of the initial alignment is to solve the carrier inertial system b at the initial moment 0 Navigation inertial system n with initial time 0 The attitude transformation relation of (1), i.e.
First, a local gravity acceleration vector is calculated at n 0 The projection of the system is:
wherein,
for the local gravity acceleration vector at n 0 The value of (a); g n Is a constant vector, g n ＝[0 0 -g] T G represents the value of the local gravitational acceleration, and:
wherein L represents the local geographic latitude, ω ie Representing the local rotation angular velocity. Due to the fact that
Is constant, i.e. n is relative to n 0 The rotation is fixed axis, which can be solved by the above formula:
where t denotes the time when the initial alignment is performed and I denotes a unit quaternion. Therefore, the method comprises the following steps:
firstly, calculating the specific force output by the accelerometer at b 0 Projection of the system:
wherein:
Finally, the relationship is transformed through the posture
Establishing a relation between the local gravity acceleration and the accelerometer output specific force measurement to obtain:
in the formula, f b Is the output of the accelerometer. Theoretically, as long as local gravity acceleration and accelerometer output specific force measurement values at two moments are obtained, a double-vector attitude determination method can be used for solving
However, to reduce the effect of accelerometer noise interference, equation (8) is integrated during the initial alignment process, i.e.:
wherein, 0 < t 1 ＜t 2 And usually take t 1 ＝t 2 /2. According to the double-vector attitude determination method, the following can be obtained:
due to the fact that
The matrix is an attitude matrix at the initial time of alignment, and in order to obtain an attitude matrix at the end time of coarse alignment, the following formula can be used for calculation:
wherein,
and &>
Determined by equations (4) and (7), respectively.
Obtaining a course angle based on the self initial attitude information and the gyroscope output, and outputting the course angle as course output;
according to the rigid body rotation theory, the differential equation corresponding to the quaternion converted from the carrier coordinate system (system b) to the navigation coordinate system (system n) is as follows:
in the formula,
is the derivative of the attitude quaternion; w is a four-dimensional antisymmetric array operation associated with a quaternion operation; />
The projection of the rotation angular velocity of the strapdown inertial navigation relative to the navigation coordinate system under a carrier coordinate system is obtained; q is an attitude quaternion. Under the condition of a static base>
For a quaternion differential equation, a fourth-order Runge-Kutta method is adopted for solving, the quaternion at the initial moment is determined according to an attitude matrix obtained by initial alignment, and the conversion relation between the attitude matrix and the quaternion is as follows:
the fourth-order Runge-Kutta method has the following calculation formula:
in the formula, t k Represents a sampling instant; h denotes a sampling interval.
According to the relation between the quaternion and the Euler angle, a calculation result of the heading angle psi is given:
the heading angle obtained by the equation (17) is directly output as the heading.
Obtaining a pitch angle and a yaw angle based on accelerometer output and local gravity acceleration, performing low-pass filtering on the pitch angle and the yaw angle, and outputting the pitch angle and the yaw angle after the low-pass filtering as horizontal postures to realize posture measurement;
the horizontal attitude angle is directly calculated by adopting the output of the accelerometer and the gravity vector, so that the noise of the accelerometer can directly influence the calculation precision. Considering the filtering effect and the delay size, the finally designed filter parameters are as follows:
the passband cut-off frequency is 1HZ, the stopband cut-off frequency is 10HZ, the passband gain is 1dB, and the stopband gain is-80 dB. Its corresponding discrete transfer function has the form of
The accelerometer output at each moment can be processed by converting the discrete transfer function shown in the formula (18) into a differential equation to obtain the processed accelerometer output
According to the relationship between the accelerometer output after the low-pass filtering processing and the gravity acceleration vector, the following can be obtained:
the formula (19) can be developed to obtain:
in the formula, theta is a pitch angle; gamma is a roll angle;
and &>
Respectively outputting the accelerometer after low-pass filtering processing of an X axis, a Y axis and a Z axis; g is the local gravitational acceleration.
The calculation formula of the horizontal (pitch angle and yaw angle) is directly obtained from equation (20):
the heading angle ψ obtained by equation (17) and the pitch angle and yaw angle obtained by equation (21) are used as outputs of the attitude reference system.
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (9)
1. A short-time high-precision attitude keeping method is characterized by comprising the following steps:
acquiring gyroscope output and accelerometer output;
obtaining self initial attitude information based on the accelerometer output and the local gravity acceleration;
obtaining a course angle based on the self initial attitude information and the gyroscope output, and outputting the course angle as a course;
and obtaining a pitch angle and a yaw angle based on the accelerometer output and the local gravitational acceleration, performing low-pass filtering on the pitch angle and the yaw angle, and outputting the pitch angle and the yaw angle after the low-pass filtering as a horizontal posture so as to realize posture measurement.
2. The short-term high-precision attitude keeping method according to claim 1, characterized in that the gyro output is:
wherein, b is a carrier coordinate system; i is an inertial coordinate system;
and &>
Gyroscope angular velocity outputs for the X-axis, Y-axis, and Z-axis, respectively, with T being the transpose.
3. The short term high accuracy pose maintenance method of claim 1, wherein the accelerometer output is:
wherein,
and &>
The specific force output of the accelerometer is shown for the X, Y and Z axes, respectively.
4. The short-term high-precision attitude keeping method according to claim 1, wherein the self initial attitude information is obtained by:
calculating the projection of the navigation inertial system of the vector of the local gravity acceleration at the initial moment;
calculating the projection of the specific force output by the accelerometer on the carrier inertia system at the initial moment;
and obtaining the self initial attitude information by adopting a double-vector attitude determination method based on the projection of the local gravity acceleration vector in the navigation inertial system at the initial moment and the projection of the specific force output by the accelerometer in the carrier inertial system at the initial moment.
5. The short-term high-precision attitude keeping method according to claim 1, wherein the course angle is obtained by:
constructing a quaternion differential equation based on the self initial attitude information and the gyroscope output;
and solving by adopting a fourth-order Runge-Kutta method based on the quaternion differential equation to obtain the course angle.
6. The short-term high-precision attitude keeping method according to claim 5, wherein the quaternion differential equation is:
in the formula,
is the derivative of the attitude quaternion; w is a four-dimensional antisymmetric array operation associated with a quaternion operation; />
For strapdown inertial navigation relative to navigation coordinatesProjecting the rotation angular speed of the system under a carrier coordinate system; q is an attitude quaternion.
7. The short-term high-precision posture maintaining method according to claim 5, wherein the fourth-order Runge-Kutta method is calculated by the formula:
in the formula, t k Represents a sampling instant; h represents a sampling interval; k is a radical of 1 -k 4 The average slope of the quaternion differential equation at different times.
8. The short-term high-precision attitude keeping method according to claim 1, wherein parameters of the low-pass filtering process are set to: the passband cut-off frequency is 1HZ, the stopband cut-off frequency is 10HZ, the passband gain is 1dB, and the stopband gain is-80 dB.
9. The short-term high-precision attitude keeping method according to claim 1, wherein the pitch angle and the yaw angle are:
in the formula, theta is a pitch angle; gamma is a roll angle;
and &>
Respectively outputting accelerometer after low-pass filtering treatment of an X axis, a Y axis and a Z axis; g is the local gravitational acceleration. />
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