CN112344964B - Carrier track simulation design method of strapdown inertial navigation system - Google Patents
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Abstract
The invention relates to a carrier track simulation design method of a strapdown inertial navigation system, which comprises the steps of establishing a coordinate system of the strapdown inertial navigation system; establishing a laser gyro error model and an accelerometer error model; establishing and solving a system differential equation to obtain system attitude, speed, position, gyro angle increment and specific force increment addition information so as to obtain inertial output information in a track running process; and acquiring a carrier motion track and generating carrier motion track data. The method sets the motion track of the carrier according to the needs of the system through mathematical modeling and computer simulation, simulates various different navigation states of the carrier under the real condition, simultaneously generates navigation data under the current condition of the carrier, comprises information of the position, the speed, the attitude and the like of a carrier under the navigation system, and outputs the angular increment and the speed increment data of a system gyroscope and an accelerometer under the corresponding motion state in real time, is used for supporting the simulation, the error analysis and the performance evaluation of the strapdown inertial navigation system, and has certain engineering practice application value.
Description
Technical Field
The invention belongs to the technical field of inertial navigation, relates to a strapdown inertial navigation system, and particularly relates to a carrier track simulation design method of the strapdown inertial navigation system.
Background
In an inertial navigation system, a strapdown inertial navigation system has the advantages of simple structure, light weight, small volume, low power consumption, convenience in maintenance and the like, so that the strapdown inertial navigation system is widely applied to various fields of sea, land, air, sky, people and the like. In the process of developing a strapdown inertial navigation system, a large amount of carrier operation data and inertial element (gyroscope, accelerometer) output data are often needed for supporting multiple aspects of development work such as system simulation, error analysis, performance evaluation and software design development, but are limited by aspects such as scientific research and production progress and test conditions, the carrier operation conditions under all real conditions are difficult to completely cover in the development process, and system operation output under all real conditions cannot be obtained. Therefore, how to simulate the carrier operation track and the output of the inertial instrument under the real condition as much as possible by establishing a mathematical simulation platform and apply the generated simulation data to analyze and evaluate the strapdown inertial navigation system is a problem which needs to be solved urgently at present.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a strapdown inertial navigation system carrier track simulation design method which is reasonable in design, accurate, reliable and convenient to use.
The technical problem to be solved by the invention is realized by adopting the following technical scheme:
a carrier track simulation design method of a strapdown inertial navigation system comprises the following steps:
step 1, establishing a strapdown inertial navigation system coordinate system;
step 2, establishing a laser gyro error model and an accelerometer error model;
step 3, establishing and solving a system differential equation to obtain system attitude, speed and position, gyro angle increment and specific force increment addition information, and further obtain inertia output information in the track running process;
and 4, acquiring a carrier motion track and generating carrier motion track data.
Further, the inertial strapdown inertial navigation system coordinate system includes: inertia coordinate system, earth coordinate system, navigation coordinate system, carrier coordinate system, track coordinate system and track horizontal system, wherein:
inertial coordinate system X i Y i Z i Comprises the following steps: the origin being at the center of the earth, Z i Along the earth axis, X i 、Y i In the equatorial plane of the earth, points to the direction of the fixed star and keeps unchanged;
terrestrial coordinate system X e Y e Z e Comprises the following steps: the origin is located at the center of the earth, the coordinate axis is fixedly connected with the earth, Z e Along the earth's axis, X e 、Y e Perpendicular to each other in the equatorial plane, X e Pointing to Greenwich meridian, the earth system rotates relative to the inertia system at the rotation angular rate of the earth;
navigation coordinate system X n Y n Z n Comprises the following steps: origin at the center of mass of the carrier, X n Finger east and Y n North arrow Z n Indicating the day;
vector coordinate system X b Y b Z b Comprises the following steps: origin at the center of mass of the carrier, X b To the right along the transverse axis of the carrier, Y b Forward along the longitudinal axis of the carrier, Z b Upward along the vertical axis of the carrier;
track coordinate system X t Y t Z t Comprises the following steps: x t Horizontal right, Y t Tangent to track and pointing forward, Z t And Y t In the vertical plane;
track level system X h Y h Z h Comprises the following steps: the track coordinate system is projected on a horizontal plane.
Further, the laser gyro error model established in step 2 is:
ω b ＝U g (K g N g -B 0 )
wherein, ω is b Projecting the gyroscope output angular velocity carrier system; u shape g The installation error of the gyroscope; k g Is a gyro scale factor; n is a radical of hydrogen g Outputting gyroscope pulses; b is 0 Zero bias for the gyroscope;
the accelerometer error model established in the step 2 is as follows:
f b ＝U a K a (N a -A 0 )
wherein f is b Outputting a specific force carrier system projection for the accelerometer; u shape a Mounting errors for the accelerometer; k a Scaling a factor for the accelerometer; n is a radical of a Outputting the accelerometer pulse; a. The 0 Zero offset for the accelerometer.
Further, the system differential equation established in step 3 includes a track differential equation and an instrument inertial information differential equation, the track differential equation includes an attitude differential equation, a velocity differential equation and a position differential equation, and the instrument inertial information differential equation includes a gyro output differential equation and an accelerometer output differential equation; wherein
The attitude differential equation is:
the velocity differential equation:
wherein,
the position differential equation:
the gyro output differential equation is:
wherein:
the accelerometer outputs a differential equation:
setting: x (t) = [ theta gamma psi V E V N V U L λ h Δθ ΔV] T ，
Then the system track parameter differential equation:
solving by fourth-order Runge-Kutta
A differential equation is used for obtaining the attitude, the speed and the position of the system, the gyro angle increment and the added specific force increment information; obtaining inertial output information in a track running process by utilizing the gyro angle increment and the added meter specific force increment information through a meter error model;
in the above formula, theta is carrier pitch angle, gamma is carrier roll angle, psi is carrier course angle, and V is n For navigation down speed V n 、V E East speed, V N Is north speed, V U Vertical speed, lambda is longitude under the navigation system, L is latitude under the navigation system, h is altitude under the navigation system, omega (t) is attitude change, a t (t) is acceleration.
Further, the specific implementation method of step 4 is as follows: selecting different carrier attitude changes omega (t) and accelerations a according to different running states t (t) as an input value, solving a system differential equation according to the input motion time and the control parameters to obtain a corresponding carrier motion track and generate carrier motion track data; wherein the operation mode and ω (t), a t (t) the input correspondence is as follows:
when the carrier is static or moves linearly at a uniform speed: the attitude change and the acceleration value are both 0; then the track generator inputs:
when the carrier moves in an acceleration or deceleration mode: the attitude change of the carrier is zero, the carrier has a constant acceleration a along the advancing direction of the track coordinate system, and if the required acceleration and deceleration movement is carried out along the advancing direction y, the track generator inputs:
when the carrier turns, the speed when the carrier turns is set as v, the heading angular speed omega of the carrier gradually increases from 0 psi to t time, and then the track generator inputs:
when the carrier ascends or descends, the speed of the carrier in the advancing direction of the track is kept unchanged, the ascending or descending process of the carrier can be regarded as that the carrier makes circular motion on a vertical plane, the time for the carrier pitch angle to gradually increase from 0 to theta at an angular rate omega is t, and then the track generator inputs:
the invention has the advantages and positive effects that:
the method sets the motion track of the carrier according to the system requirement through mathematical modeling and computer simulation, simulates various navigation states of the carrier under the real condition as much as possible, simultaneously generates navigation data under the current condition of the carrier, comprises information such as the position, the speed, the attitude and the like of a carrier under a navigation system, and outputs angle increment and speed increment data of a gyroscope and an accelerometer of the system under the corresponding motion state in real time, so as to support the simulation, error analysis and performance evaluation work of the strapdown inertial navigation system. For example, in a vehicle-mounted state, the running states of vehicle starting, accelerating, decelerating, straight running, backing, turning, ascending, descending and the like can be simulated, and meanwhile, the information of theoretical position, speed, attitude, angle increment, speed increment and the like of the inertial navigation system is output, so that the system performance evaluation and error analysis are facilitated, and the system has a certain engineering practice application value.
Drawings
FIG. 1 is a detailed path track graph provided by an embodiment of the present invention;
FIG. 2 is a comparison of navigation results of the present invention.
Detailed Description
The embodiments of the present invention will be described in detail with reference to the accompanying drawings.
A strapdown inertial navigation system carrier track simulation design method comprises the following steps:
step 1, establishing a coordinate system of a strapdown inertial navigation system, wherein the coordinate system comprises: inertia coordinate system, earth coordinate system, navigation coordinate system, carrier coordinate system, track coordinate system and track horizontal system, wherein:
1. inertial system of coordinates (i system) X i Y i Z i : the origin being at the center of the earth, Z i Along the earth's axis, X i 、Y i In the equatorial plane of the earth, points to the direction of the stars and remains unchanged.
2. Terrestrial coordinate system (e system) X e Y e Z e : the origin is located at the center of the earth, the coordinate axes are fixedly connected with the earth, Z e Along the earth's axis, X e 、Y e Perpendicular to each other in the equatorial plane, X e Pointing at the greenwich meridian, the earth system rotates at the earth rotation angular rate relative to the inertial system.
3. Navigation coordinate system (n system) X n Y n Z n : origin at the center of mass of the carrier, X n East and west of the fingers n North arrow Z n It refers to the geographic coordinate system of the heaven, namely the northeast.
4. Vector coordinate system (system b) X b Y b Z b : origin at the center of mass of the carrier, X b To the right along the transverse axis of the carrier, Y b Forward along the longitudinal axis of the carrier, Z b Along the vertical axis of the carrier.
5. Track coordinate system (t system) X t Y t Z t ：X t Horizontal to the right, Y t Tangent to track and pointing forward, Z t And Y t In the vertical plane.
6. Track level system (h system) X h Y h Z h : the projection of the track coordinate system on the horizontal plane is the h system.
Step 2, adopting a laser gyroscope and a quartz pendulum accelerometer and establishing an instrument error model, wherein the specific error model is as follows:
1. laser gyro error model
Namely: omega b ＝U g (K g N g -B 0 ) (2-2)
Wherein: omega b Projecting the gyroscope output angular velocity carrier system; u shape g The installation error of the gyroscope; k g Is a gyro scale factor; n is a radical of g Outputting gyroscope pulses; b is 0 Is the gyro zero offset.
2. Accelerometer error model
Namely: f. of b ＝U a K a (N a -A 0 ) (2-4)
Wherein: f. of b Outputting a specific force carrier system projection for the accelerometer; u shape a Mounting errors for the accelerometer; k a Scaling a factor for an accelerometer; n is a radical of hydrogen a Pulse output for the accelerometer; a. The 0 Zero offset for the accelerometer.
And 3, establishing and solving a system differential equation to obtain the attitude, speed and position of the system, the gyro angle increment and the adding table specific force increment information, and further obtain inertia output information in the track running process.
Because the actual attitude, the position, the speed and the like of the carrier can be obtained by solving the system differential equation by using the Runge-Kutta and the inertial output information of the system instrument is generated, the step establishes the system differential equation which mainly comprises two parts: one part is carrier attitude Atti (pitch angle theta rolling angle gamma course angle psi) and speed V under the navigation system n (Dongshu V) E North speed V N Vertical velocity V U ) The differential equation of the position Pos (longitude lambda latitude L height h) under the navigation system is mainly used for solving the navigation track of the carrier; another part is laserThe gyro angular velocity increment and the accelerometer specific force increment differential equation are mainly used for generating instrument inertia information. The inertial information of the instrument can be used as data input of a strapdown navigation algorithm to carry out navigation calculation, the obtained result is compared with the actual running track of the carrier and is used for system error analysis, and meanwhile, the running track information of the carrier can be used for simulating external reference information such as a satellite navigation system, a speedometer and a log after errors and white noise are added.
1. A trajectory differential equation comprising:
attitude differential equation:
velocity differential equation:
wherein:
position differential equation:
2. differential equation of instrument inertial information
Gyro output differential equation:
wherein:
the accelerometer outputs a differential equation:
in summary, a system track parameter differential equation can be established
X(t)＝[θ γ ψ V E V N V U L λ h Δθ ΔV] T ，
According to the formulas (3-1) to (3-5), there are:
solving by fourth-order Runge-Kutta
And (4) obtaining the required system attitude, speed and position, the gyro angle increment and the addition table specific force increment information by a differential equation. And obtaining the pulse output of the instrument in the track running process by utilizing the gyro angle increment and the added specific force increment information according to an instrument error model (formulas 2-1 and 2-3).
And 4, acquiring a carrier motion track to generate carrier motion track data.
For vehicles such as vehicles and ships, the system travels on the earth surface, and the operation of the vehicle comprises movement modes such as static, constant speed, acceleration/deceleration, turning, ascending/descending and the like. The invention adopts attitude change omega (t) and accelerationDegree a t (t) variation as input, selecting different omega (t) and alpha according to different required running states t (t) inputting values, and solving a system differential equation according to the input motion time and the control parameters to obtain a corresponding carrier motion track and generate carrier motion track data. Specific operation mode and omega (t), a t (t) the input correspondence is as follows:
1. the carrier is static or moves linearly at a uniform speed: when the carrier is static or does uniform linear motion, the attitude change and the acceleration value are both 0. Then the track generator inputs:
2. acceleration or deceleration movement of the carrier: when the carrier is accelerated or decelerated, the attitude change of the carrier is zero, the carrier has a constant acceleration a along the advancing direction of a track coordinate system, and if the carrier is accelerated or decelerated along the y direction of the advancing direction, the track generator inputs:
3. turning motion of the carrier: when the carrier makes turning motion, the turning of the carrier can be simplified into the change of the course angle. In the motion process, the speed when turning is set as v, the carrier heading angular speed omega is gradually increased from 0 psi to t time, and then the track generator inputs:
4. carrier ascending (or descending) motion: when the carrier does ascending or descending motion, the speed of the carrier in the advancing direction along the track is kept unchanged, the ascending process of the carrier can be regarded as that the carrier does circular motion on a vertical plane, and the time for the carrier pitch angle to gradually increase from 0 to theta at an angular rate omega is t, then the track generator inputs:
the descending process analysis is similar to the ascending process analysis.
The carrier track simulation design function of the strapdown inertial navigation system can be realized through the steps.
The invention is verified by a simulation test as follows:
according to the scheme, the vehicle running path is simulated by combining with a certain project strapdown inertial navigation vehicle-mounted test, the simulated running track comprises the processes of stillness, acceleration, turning, uphill, deceleration, stopping and the like, the correctness of the track design method is verified, and a specific path track diagram is shown in figure 1.
The inertial instrument information (gyro angle increment and accelerometer speed increment) generated by the track generator is used as the input of a navigation algorithm to check whether the navigation solution scheme and the design software function are correct or not, the output result is shown in figure 2, the upper diagram is a running path, the lower diagram is the navigation position output, and the navigation position output result is consistent with a simulation path as shown in the figure. Meanwhile, if errors or noises are added in the information of the inertial instrument, the obtained information of the inertial instrument can also be used for error analysis and performance evaluation of the strapdown inertial navigation system.
Through the vehicle-mounted test of the strapdown inertial navigation system, a specific test path can be simulated, and the correctness of the flight path design method is verified. Meanwhile, navigation calculation is carried out according to the generated instrument inertia information, and the function and performance of the inertial system navigation algorithm are tested, so that the method can be widely applied to support system simulation, error analysis and functional performance verification, and has certain practical significance for engineering practice.
It should be emphasized that the embodiments described herein are illustrative rather than restrictive, and thus the present invention is not limited to the embodiments described in the detailed description, but also includes other embodiments that can be derived from the technical solutions of the present invention by those skilled in the art.
Claims (1)
1. A strap-down inertial navigation system carrier track simulation design method is characterized by comprising the following steps: the method comprises the following steps:
step 1, establishing a strapdown inertial navigation system coordinate system, wherein the inertial strapdown inertial navigation system coordinate system comprises: inertia coordinate system, earth coordinate system, navigation coordinate system, carrier coordinate system, track coordinate system and track horizontal system, wherein:
inertial coordinate system X i Y i Z i Comprises the following steps: the origin being at the center of the earth, Z i Along the earth axis, X i 、Y i In the equatorial plane of the earth, points to the direction of the fixed star and keeps unchanged;
terrestrial coordinate system X e Y e Z e Comprises the following steps: the origin is located at the center of the earth, the coordinate axes are fixedly connected with the earth, Z e Along the earth's axis, X e 、Y e Perpendicular to each other in the equatorial plane, X e Pointing to the Greenwich meridian, wherein the earth system rotates relative to the inertia system at the rotation angular rate of the earth;
navigation coordinate system X n Y n Z n Comprises the following steps: origin is located at the center of mass of the carrier, X n Finger east and Y n North arrow Z n Indicating the day;
vector coordinate system X b Y b Z b Comprises the following steps: origin at the center of mass of the carrier, X b To the right along the transverse axis of the carrier, Y b Forward along the longitudinal axis of the carrier, Z b Upward along the vertical axis of the carrier;
track coordinate system X t Y t Z t Comprises the following steps: x t Horizontal right, Y t Tangent to track and pointing forward, Z t And Y t In the vertical plane;
track level system X h Y h Z h Comprises the following steps: projecting the track coordinate system on a horizontal plane;
step 2, establishing a laser gyro error model and an accelerometer error model, wherein:
the laser gyro error model is as follows:
ω b ＝U g (K g N g -B 0 )
wherein, ω is b Projecting the gyroscope output angular velocity carrier system; u shape g The installation error of the gyroscope; k g Is a gyro scale factor; n is a radical of hydrogen g Outputting gyroscope pulses; b is 0 Zero bias for the gyroscope;
the accelerometer error model is:
f b ＝U a K a (N a -A 0 )
wherein f is b Outputting a specific force carrier system projection for the accelerometer; u shape a Mounting errors for the accelerometer; k a Scaling a factor for an accelerometer; n is a radical of a Pulse output for the accelerometer; a. The 0 Zero offset for the accelerometer;
step 3, establishing and solving a system differential equation to obtain system attitude, speed and position, gyro angle increment and specific force increment addition information, and further obtain inertia output information in the track running process;
the system differential equation comprises a track differential equation and an instrument inertia information differential equation, the track differential equation comprises an attitude differential equation, a speed differential equation and a position differential equation, and the instrument inertia information differential equation comprises a gyro output differential equation and an accelerometer output differential equation; wherein
The attitude differential equation is:
the velocity differential equation:
wherein,
the position differential equation:
the gyro output differential equation is:
wherein:
the accelerometer outputs a differential equation:
setting: x (t) = [ theta gamma psi V E V N V U L λ h Δθ ΔV] T ，
Then the system track parameter differential equation:
solving by fourth order Runge-Kutta
A differential equation is used for obtaining the attitude, the speed and the position of the system, the gyro angle increment and the added specific force increment information; obtaining inertial output information in a track running process by utilizing the gyro angle increment and the added meter specific force increment information through a meter error model;
in the above formula, theta is carrier pitch angle, gamma is carrier roll angle, psi is carrier course angle, and V is n For navigation down-system speeds Vn, V E Dongshu, V N Is north speed, V U Vertical velocity, lambda is longitude under navigation system, L is latitude under navigation system, h is altitude under navigation system, omega (t) is attitude change, a t (t) is acceleration;
step 4, acquiring a carrier motion track and generating carrier motion track data, wherein the specific method comprises the following steps:
selecting different carrier attitude changes omega (t) and accelerations a according to different running states t (t) as an input value, solving a system differential equation according to the input motion time and the control parameters to obtain a corresponding carrier motion track and generate carrier motion track data; wherein the operation mode and ω (t), a t (t) the input correspondence is as follows:
when the carrier is static or moves linearly at a constant speed: the attitude change and the acceleration value are both 0; then the track generator inputs:
when the carrier moves in an acceleration or deceleration mode: the attitude change of the carrier is zero, the carrier has a constant acceleration a along the advancing direction of the track coordinate system, and if the required acceleration and deceleration movement is carried out along the advancing direction y, the track generator inputs:
when the carrier turns, the speed when the carrier turns is set as v, the heading angular speed omega of the carrier gradually increases from 0 psi to t time, and then the track generator inputs:
when the carrier moves upwards or downwards, the speed of the carrier in the advancing direction of the track keeps unchanged, the ascending or descending process of the carrier can be regarded as that the carrier makes circular motion on a vertical plane, and the time for the carrier pitch angle to gradually increase from 0 to theta at an angular rate omega is t, then the track generator inputs:
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