CN112733314B - Inertial sensor data simulation method - Google Patents
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Abstract
The invention provides a data simulation method of an inertial sensor, which belongs to the field of inertial sensor data simulation and comprises the following steps: collecting data; step two: establishing an inertial sensor output error model; step three: estimating inertial sensor fixing error; step four: calculating a theoretical output value of the inertial sensor; step five: extracting random errors of the inertial sensor; step six: generating inertial sensor analog data; the invention solves the problem that the random error of the inertial sensor data simulation in the prior art can not completely reflect the random error characteristic of a real inertial sensor, can reflect the random error characteristic of the inertial sensor more truly, and can meet the requirements of scientific research and teaching in the field of inertial navigation.
Description
Technical Field
The invention relates to the field of inertial sensor data simulation, in particular to an inertial sensor data simulation method.
Background
The inertial sensor is the core of an inertial navigation system, and comprises three orthogonally mounted gyros and three orthogonally mounted accelerometers. The high-precision inertial navigation system is expensive and high in test cost, and can generate inertial sensor data through a simulation algorithm by using an inertial navigation simulator in order to meet the requirements of scientific research and teaching in the field of inertial navigation. The key factor for determining the performance of the inertial navigation simulator is whether the inertial sensor data simulation algorithm can accurately reflect the error characteristics of a real inertial sensor, the inertial sensor errors comprise fixed errors and random errors, the fixed errors can be described and simulated by an algebraic model in a determinable mode, and the random errors can be only approximately described and simulated by a statistical model.
The currently used inertial sensor data simulation method is mainly based on a mathematical model, and has the defect that the simulated random error cannot completely reflect the random error characteristic of a real inertial sensor, so that a new data simulation algorithm is needed, and the random error characteristic of the inertial sensor can be more truly reflected.
Disclosure of Invention
In view of the above-mentioned shortcomings of the prior art, the present invention aims to provide an inertial sensor data simulation method for solving the problem that the random error of the inertial sensor data simulation in the prior art cannot fully reflect the random error characteristics of the real inertial sensor.
The invention provides an inertial sensor data simulation method, which comprises the following steps:
the method comprises the following steps: data acquisition
The data acquisition object is an inertial navigation system, the inertial navigation system is installed on a three-axis turntable, the three-axis turntable rotates according to a system-level calibration rotation arrangement scheme, and the inertial sensor output data of the inertial navigation system in a state of following the rotation of the turntable is acquired;
step two: establishing an inertial sensor output error model
Defining a carrier coordinate system b, establishing an inertial sensor output error model, and calculating a fixed error and a random error of the inertial sensor;
the carrier coordinate system b is an orthogonal coordinate system, the X axis of the carrier coordinate system b points to the forward direction of the inertial navigation, the Y axis of the carrier coordinate system b points to the right direction of the inertial navigation, and the Z axis of the carrier coordinate system b, the X axis and the Y axis form an orthogonal coordinate system according to the right-hand rule;
step three: inertial sensor fixation error estimation
Establishing a system-level calibration Kalman filter, and processing the output data of the inertial sensor in the step one by adopting the Kalman filter to obtain an estimated value of the fixed error of the inertial sensor in the step two;
step four: inertial sensor theoretical output value calculation
Calculating theoretical output values of the inertial sensors according to the system-level calibration rotation arrangement scheme in the step one;
step five: extracting inertial sensor random errors
According to the output error model of the inertial sensor in the second step, deducting the fixed error estimation value of the inertial sensor obtained in the third step and the theoretical output value of the inertial sensor obtained in the fourth step from the output data of the inertial sensor collected in the first step to obtain a calculation result;
filtering the obtained calculation result to eliminate extra noise caused by the motion of the three-axis turntable and obtain the time length t w The inertial sensor random error of (1);
step six: generating inertial sensor analog data
Setting the simulation motion state of the carrier and the simulation time as t d Generating a theoretical output value of the inertial sensor according to the simulated motion state of the carrier;
if t w ＞t d And if so, randomly selecting the time length t from the random error data obtained in the step five d The data section is added with the theoretical output value of the inertial sensor generated in the step to obtain analog data of the inertial sensor;
if t w ＜t d Interpolating the random error data obtained in the fifth step into the data with the duration of t by using a spline interpolation algorithm d And adding the data segment of (1) and the theoretical output value of the inertial sensor generated in the step to obtain analog data of the inertial sensor.
In an embodiment of the invention, the inertial sensor error model includes a gyro output error model and an accelerometer output error model.
In an embodiment of the present invention, the gyro output error model formula is:
wherein the content of the first and second substances,
are respectively X-axis, Y-axis and Z-axis gyroscopeA spiral output error; b is gx ,B gy ,B gz Zero offset errors of gyros of an X axis, a Y axis and a Z axis respectively; s gx ,S gy ,S gz Gyroscope scale factor errors of an X axis, a Y axis and a Z axis respectively; m gyx ,M gzy ,M gzx Is a gyro mounting error.
In an embodiment of the present invention, the accelerometer output error model formula is:
wherein the content of the first and second substances,
respectively outputting errors of accelerometers along an X axis, a Y axis and a Z axis; b ax ,B ay ,B az Zero offset errors of accelerometers are respectively an X axis, a Y axis and a Z axis; s ax ,S ay ,S az The accelerometer scale factor errors of an X axis, a Y axis and a Z axis respectively; m ayx ,M axy ,M ayz ,M azy ,M axz ,M azx An accelerometer installation error.
In an embodiment of the present invention, in the fifth step, a high-pass filter is adopted to perform filtering processing on the obtained calculation result.
As described above, the inertial sensor data simulation method of the present invention has the following beneficial effects: the method solves the problem that the random error of the inertial sensor data simulation in the prior art cannot completely reflect the random error characteristic of a real inertial sensor, can reflect the random error characteristic of the inertial sensor more truly, and can meet the requirements of scientific research and teaching in the field of inertial navigation.
Drawings
FIG. 1 is a flow chart of a method disclosed in an embodiment of the present invention.
Fig. 2 is a diagram showing the estimation result of the gyro zero offset error in the fourth step disclosed in the embodiment of the present invention.
Fig. 3 is a diagram showing the estimation result of the gyro scale factor error in the fourth step disclosed in the embodiment of the present invention.
Fig. 4 is a diagram showing the estimation result of the gyro mounting error in the fourth step disclosed in the embodiment of the present invention.
Fig. 5 is a diagram showing the estimation result of the zero offset error of the accelerometer in the fourth step disclosed in the embodiment of the invention.
FIG. 6 is a graph showing the results of the four steps disclosed in the embodiment of the present invention for estimating the error of the accelerometer scale factor.
Fig. 7 is a diagram showing the results of estimating the mounting error of the accelerometer in the fourth step disclosed in the embodiment of the invention.
Fig. 8 shows a gyro random error map extracted in step five disclosed in the embodiment of the present invention.
FIG. 9 is a graph of random error of the accelerometer extracted in step five disclosed in the embodiments of the present invention.
Fig. 10 shows a vehicle trajectory map set for step six disclosed in the example of the present invention.
Fig. 11 shows a graph of gyro output data generated in step six disclosed in the embodiment of the present invention.
Figure 12 is a graph showing accelerometer output data generated for step six as disclosed in an embodiment of the present invention.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It is to be noted that the features in the following embodiments and examples may be combined with each other without conflict.
It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention, and the components related to the present invention are only shown in the drawings rather than drawn according to the number, shape and size of the components in actual implementation, and the type, quantity and proportion of the components in actual implementation may be changed freely, and the layout of the components may be more complicated.
As shown in fig. 1, the present invention provides an inertial sensor data simulation method, comprising the steps of:
the method comprises the following steps: data acquisition
The data acquisition method comprises the following steps that a data acquisition object is an inertial navigation system (IMU), the inertial navigation system is installed on a three-axis rotary table, the three-axis rotary table rotates according to a system-level calibration rotation arrangement scheme shown in a table 1, and data output by an inertial sensor of the inertial navigation system in a state of rotating along with the three-axis rotary table are acquired;
TABLE 1
Step two: defining a carrier coordinate system b, wherein the carrier coordinate system b is an orthogonal coordinate system, the X axis of the carrier coordinate system b points to the forward direction of the inertial navigation system in the step I, the Y axis of the carrier coordinate system b points to the right direction of the inertial navigation system in the step I, and the Z axis of the carrier coordinate system b forms an orthogonal coordinate system with the X axis and the Y axis according to a right-hand rule; an output error model of the inertial sensor is established, under a carrier coordinate system b, the output error model of the gyroscope is shown as a formula (1), and the output error model of the accelerometer is shown as a formula (2):
wherein the content of the first and second substances,
output errors of the axis gyros of X axis, Y axis and Z axis respectively; b is gx ,B gy ,B gz Gyro zero offset error of X axis, Y axis and Z axis respectively；S gx ,S gy ,S gz Gyroscope scale factor errors of an X axis, a Y axis and a Z axis respectively; m is a group of gyx ,M gzy ,M gzx The gyro installation error is obtained;
accelerometer output errors of an X axis, a Y axis and a Z axis respectively; b is ax ,B ay ,B az Zero offset errors of the accelerometers are respectively an X axis, a Y axis and a Z axis; s ax ,S ay ,S az Accelerometer scale factor errors for the X, Y and Z axes, respectively; m ayx ,M axy ,M ayz ,M azy ,M axz ,M azx Mounting errors for the accelerometer;
step three: establishing a system-level calibration Kalman filter, wherein a state vector of the Kalman filter is shown as a formula (3):
wherein, δ θ, δ γ, δ φ are pitch angle error, roll angle error and course angle error respectively; delta v E ,δv N ,δv U East-direction speed error, north-direction speed error and sky-direction speed error respectively; δ L, δ λ, δ h are latitude error, longitude error and altitude error, respectively;
the Kalman filter state equation is established as shown in formula (4):
wherein F is a Kalman filter system model, and q is system noise; h is a Kalman filter observation equation, ν is observation noise;
f is defined as follows:
wherein the content of the first and second substances,
and
projection components of the inertial navigation coordinate system relative to the rotation angular speed of the inertial space in the east direction, the north direction and the sky direction are shown in formula (7);
wherein R is N And R E The radius of the meridian and the radius of the prime, L and h are the latitude and height of the carrier;
wherein v is N And v E North and east, respectively, speeds of the inertial navigation system ie The rotational angular velocity of the earth;
wherein the content of the first and second substances,
a direction cosine matrix transformed from the carrier coordinate system b to the navigation coordinate system n;
F 15 ＝0 3×3 (10)
wherein the content of the first and second substances,
and
respectively projection of gyroscope outputs of an X axis, a Y axis and a Z axis in a b system of a carrier coordinate system;
F 17 ＝0 3×9 (12)
wherein f is E 、f N And f U Projecting the specific force measured by the accelerometer in the east direction, the north direction and the sky direction respectively;
wherein v is U Is the speed of the vector in the direction of the day.
F 24 ＝0 3×3 (16)
F 26 ＝0 3×6 (18)
Wherein the content of the first and second substances,
and
the projections of accelerometer outputs of an X-axis accelerometer, a Y-axis accelerometer and a Z-axis accelerometer in a b system of a carrier coordinate system I 3×3 Is a 3-order identity matrix;
F 31 ＝0 3×3 (20)
F 34 ＝0 3×3 (23)
F 35 ＝0 3×3 (24)
F 36 ＝0 3×6 (25)
F 37 ＝0 3×9 (26)
F 4 ＝0 21×30 (27)
taking the position of the three-axis turntable as an observed quantity, and considering that the real speed of the inertial navigation system is 0 when in calibration, obtaining an observation equation as a formula (28)
Wherein the content of the first and second substances,
and
respectively measuring the east speed, the north speed and the sky speed of the carrier by an inertial navigation system;
and
respectively, inertial navigation system measurementsVector latitude, longitude and altitude of the quantity; l is 0 、λ 0 And h 0 Respectively the latitude, longitude and altitude of the position of the three-axis turntable; 0 m×n Is an m × n dimensional zero matrix:
performing system-level calibration calculation by using Kalman filters established by formulas (3) to (29), estimating the fixed error of the inertial sensor to obtain a fixed error estimated value, wherein the method comprises the following steps: a gyro zero-offset error estimation value, a gyro scale factor error estimation value, a gyro installation error estimation value, an accelerometer zero-offset error estimation value, an accelerometer scale factor error estimation value and an accelerometer installation error estimation value, wherein the fixed error estimation results of the inertial sensors are shown in figures 2-7 and table 2;
TABLE 2
Step four: calculating a theoretical output value of the inertial sensor;
calculating to obtain the theoretical output value of the X-axis gyroscope according to the system-level calibration rotation arrangement scheme in the table 1
Theoretical output value of Y-axis gyroscope
Theoretical output value of Z-axis gyroscope
Theoretical output value of X-axis accelerometer
Theoretical output value of Y-axis accelerometer
And theoretical output value of Z-axis accelerometer
And a theoretical output value of the accelerometer;
the theoretical output value calculation formulas of the gyroscope and the accelerometer are prior art in the technical field of inertia, and therefore are not specifically described.
Step five: extracting random errors of the inertial sensor;
substituting the inertial sensor fixed error obtained in the third step and the inertial sensor theoretical output value obtained in the fourth step into a formula (30) and a formula (31) according to the inertial sensor error models (1) and (2) to obtain a random error of the inertial sensor;
wherein, the first and the second end of the pipe are connected with each other,
the extracted gyro random errors of the X-axis, Y-axis and Z-axis, respectively, are shown in fig. 8;
the random errors of the accelerometers are extracted for the X-axis, Y-axis and Z-axis respectively, as shown in fig. 9.
Step six: generating inertial sensor analog data;
setting the simulation motion state of the carrier and the simulation time as t d =3600 s, generating inertial sensor theory from carrier simulation motion stateOutput value because of t w ＝4230＞t d Randomly selecting time length t from the random error data obtained in the step five d The data segment (c) is added to the inertial sensor output theoretical value generated in this step to obtain inertial sensor analog data, as shown in fig. 10 to 12.
In conclusion, the method and the device solve the problem that the random error of the inertial sensor data simulation in the prior art cannot completely reflect the random error characteristic of a real inertial sensor, can reflect the random error characteristic of the inertial sensor more truly, and meet the requirements of scientific research and teaching in the field of inertial navigation. Therefore, the invention effectively overcomes various defects in the prior art and has high industrial utilization value.
The foregoing embodiments are merely illustrative of the principles and utilities of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or change the above-mentioned embodiments without departing from the spirit and scope of the present invention. Accordingly, it is intended that all equivalent modifications or changes which can be made by those skilled in the art without departing from the spirit and technical spirit of the present invention be covered by the claims of the present invention.
Claims (5)
1. A method of inertial sensor data simulation, the method comprising the steps of:
the method comprises the following steps: data acquisition
The data acquisition object is an inertial navigation system, the inertial navigation system is installed on a three-axis turntable, the three-axis turntable rotates according to a system-level calibration rotation arrangement scheme, and the inertial sensor output data of the inertial navigation system in a state of following the rotation of the turntable is acquired;
step two: establishing an inertial sensor output error model
Defining a carrier coordinate system b, establishing an inertial sensor output error model, and calculating a fixed error and a random error of the inertial sensor;
the carrier coordinate system b is an orthogonal coordinate system, the X axis of the carrier coordinate system b points to the forward direction of the inertial navigation, the Y axis of the carrier coordinate system b points to the right direction of the inertial navigation, and the Z axis of the carrier coordinate system b, the X axis and the Y axis form an orthogonal coordinate system according to the right-hand rule;
step three: inertial sensor fixation error estimation
Establishing a system-level calibration Kalman filter, and processing the output data of the inertial sensor in the step one by adopting the Kalman filter to obtain an estimated value of the fixed error of the inertial sensor in the step two;
step four: inertial sensor theoretical output value calculation
Calculating theoretical output values of the inertial sensors according to the system-level calibration rotation arrangement scheme in the step one;
step five: extracting inertial sensor random errors
According to the output error model of the inertial sensor in the second step, deducting the fixed error estimation value of the inertial sensor obtained in the third step and the theoretical output value of the inertial sensor obtained in the fourth step from the output data of the inertial sensor collected in the first step to obtain a calculation result;
filtering the obtained calculation result, eliminating extra noise introduced by the movement of the three-axis turntable, and obtaining the random error of the inertial sensor with the time length t w;
step six: generating inertial sensor analog data
Setting the simulation motion state of the carrier, and setting the simulation time as t d Generating a theoretical output value of the inertial sensor according to the simulated motion state of the carrier;
if t is w ＞t d And if so, randomly selecting the time length t from the random error data obtained in the step five d The data section is added with the theoretical output value of the inertial sensor generated in the step to obtain analog data of the inertial sensor;
if t is w ＜t d Interpolating the random error data obtained in the fifth step into the data with the duration of t by using a spline interpolation algorithm d And adding the data segment of (1) and the theoretical output value of the inertial sensor generated in the step to obtain analog data of the inertial sensor.
2. The inertial sensor data simulation method of claim 1, wherein: the inertial sensor error model comprises a gyro output error model and an accelerometer output error model.
3. The inertial sensor data simulation method of claim 2, wherein: the gyro output error model formula is as follows:
wherein, the first and the second end of the pipe are connected with each other,
gyroscope output errors of an X axis, a Y axis and a Z axis respectively; b gx, B gy and B gz are respectively zero offset errors of gyros of an X axis, a Y axis and a Z axis; s gx, S gy and S gz are gyroscope scale factor errors of an X axis, a Y axis and a Z axis respectively; m gyx, M gzy and M gzx are installation errors of the gyroscope.
4. The inertial sensor data simulation method of claim 2, wherein: the accelerometer output error model formula is as follows:
wherein the content of the first and second substances,
respectively outputting errors of accelerometers along an X axis, a Y axis and a Z axis; b ax, B ay and B az are respectively zero offset errors of the accelerometers of the X axis, the Y axis and the Z axis; s ax, S ay and S az are respectively the scale factor errors of the accelerometer on the X axis, the Y axis and the Z axis; m ayx, M axy, M ayz, M azy, M axz, M azx are accelerometer mounting errors.
5. The inertial sensor data simulation method of claim 1, wherein: and step five, filtering the obtained calculation result by adopting a high-pass filter.
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Denomination of invention: A data simulation method for inertial sensors Granted publication date: 20230321 Pledgee: Chengdu financial holding Financing Guarantee Co.,Ltd. Pledgor: Chengdu anzeyou Technology Co.,Ltd. Registration number: Y2024510000037 |