CN113405563A - Inertial measurement unit alignment method - Google Patents
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Abstract
The application discloses an inertial measurement unit alignment method, which comprises the following steps: acquiring output data of an inertial device in a shaking environment; decomposing an attitude matrix based on an inertial solidification principle; solving an attitude matrix based on a double-vector attitude determination TRIAD algorithm and a recursion quaternion estimation REQUEST algorithm to obtain a coarse alignment result; establishing a Kalman filtering error model by taking a coarse alignment result obtained in a coarse alignment stage as an initial value, and performing iterative filtering alignment by using inertial device data stored at the past moment to obtain an initial alignment result; outputting an initial alignment result in a shaking environment; the problem that the alignment precision of the traditional coarse alignment method is low under the condition of large-amplitude shaking interference in the related technology can be solved; according to the initial alignment result of the vehicle-mounted positioning and orientation system under the shaking base, the method can be effectively suitable for the strong shaking interference environment, and the optimal alignment precision is realized while the alignment time is shortened.
Description
Technical Field
The invention belongs to the technical field of inertial navigation, and relates to an inertial measurement unit alignment method.
Background
As an important branch of the field of inertial navigation, the vehicle-mounted positioning and orientation system opens up wide application prospects in the fields of strategic military, commercial civilian use and the like, and plays an important role in national defense construction and national economic development. In a vehicle-mounted positioning and orientation system, an inertial navigation technology is a process of carrying out integral operation on the attitude, the speed and the position of a carrier based on information measured by an inertial sensor and is used as a core link of the inertial navigation technology, and an initial alignment task is to determine a carrier attitude matrix and provide an accurate initial integral value for navigation operation. In order to ensure the mobility of the carrier, the vehicle-mounted positioning and orientation system needs to have the capability of quickly starting a navigation task; meanwhile, the attitude misalignment angle not only affects the system error in the form of attitude information, but also reflects the system error in the acquisition of speed and position information, and directly affects the navigation precision of the system. Therefore, the initial alignment needs to achieve two key indexes of rapidity and accuracy, which are usually contradictory to each other. Therefore, developing a research for completing high-precision initial alignment in a short time is of great importance for improving the reaction capability and positioning and orientation precision of the vehicle-mounted system.
According to the principle of an alignment process, the method can be divided into a coarse alignment stage and a fine alignment stage, the attitude matrix is preliminarily solved by utilizing measurement information of an inertial sensor in the coarse alignment stage, a common method mainly comprises analytic coarse alignment and inertial system coarse alignment, the analytic coarse alignment utilizes projections of the gravity acceleration and the earth rotation angular rate in different coordinate systems to obtain the attitude matrix, and generally, the geographic position of an alignment place is known, so that the projections of the gravity acceleration and the earth rotation angular rate vector in a navigation coordinate system are also known, and the attitude matrix can be obtained through a conversion relation between the gravity acceleration and the earth rotation angular rate vector in a loading system and the navigation system.
However, the analytic coarse alignment method is only applicable to a static base environment, the method regards the attitude matrix as a constant value, and it is assumed that the gyro measurement output is the earth rotation angular rate vector and the accelerometer measurement output is the gravity acceleration vector. In fact, in a strong interference environment, the attitude matrix is not fixed, and the large interference angular rate makes it difficult to extract effective information in the gyro output, and the above assumption is no longer true. Therefore, the alignment accuracy is low in a severe environment with large interference, and effective initial alignment cannot be completed.
The inertial system rough alignment firstly decomposes the attitude matrix, and indirectly solves the attitude by using a double-vector attitude determination principle; and in the fine alignment stage, based on the initial attitude value calculated by the coarse alignment, assuming that the attitude misalignment angle is a small-angle error, and taking the inertial device error and the navigation error as observed quantities, performing optimal estimation on the misalignment angle to obtain an accurate attitude matrix.
The inertial system rough alignment method can adapt to a shaking environment, but does not effectively utilize all measurement information and cannot achieve optimal alignment precision. On the basis of the existing alignment method, how to complete high-precision initial alignment under the shaking interference environment is a key problem of focusing of the invention.
Disclosure of Invention
In order to solve the problem that the alignment precision of the traditional rough alignment method is not high under the condition of large-amplitude shaking interference in the related technology, the embodiment of the application provides an alignment method of an inertial measurement unit. The method completes coarse alignment through the TRIAD (the three-axis alignment estimation) algorithm and the REQUEST (recursive quaternion estimation) algorithm, performs Kalman filtering fine alignment based on the inertial device measurement information at the stored historical moment, and provides a combined alignment method which can be suitable for shaking and swinging environments and effectively balances alignment time and alignment accuracy. The technical scheme is as follows:
acquiring output data of an inertial device in a shaking environment;
decomposing an attitude matrix based on an inertial solidification principle;
solving the attitude matrix based on a double-vector attitude determination TRIAD algorithm and a recursion quaternion estimation REQUEST algorithm to obtain a coarse alignment result;
establishing a Kalman filtering error model by taking the coarse alignment result obtained in the coarse alignment stage as an initial value, and carrying out iterative filtering alignment by using inertial device data stored at the past moment to obtain an initial alignment result;
outputting the initial alignment result in the shaking environment.
Optionally, the decomposing of the attitude matrix based on the principle of inertial coagulation is represented by:
wherein n represents a navigational coordinate system, i.e. the local geographyA coordinate system; b represents a carrier coordinate system which is fixedly connected with the carrier;
the navigation inertial coordinate system is a coordinate system which is determined according to the inertial solidification principle by aiming at the navigation coordinate system at the initial moment;
the inertial coordinate system of the carrier is expressed and is determined according to the inertial solidification principle by aligning the carrier coordinate system at the initial moment;
representing a posture conversion matrix from a navigation inertial system to a navigation system, changing along with time, and acquiring and updating through alignment time and the resolved position information;
representing a posture conversion matrix from a carrier system to a carrier inertial system, changing along with time, and acquiring and updating through gyroscope output angular rate information;
the attitude transformation matrix representing the inertial system of the carrier to the inertial system of the navigation is a constant value matrix corresponding to the alignment starting moment;
wherein the attitude matrix
The decomposition is as follows:
in the formula ,
indicating the initial moment of alignment t0The earth coordinate system is a coordinate system determined according to the inertial coagulation principle.
Optionally, the
The solving process comprises the following steps:
using the angular velocity of the gyroscope
Projection of alternative rotation angular rates onto a carrier system
From the alignment start time, the quaternion is resolved and updated in each sampling interval;
completing the attitude matrix according to the conversion relation between the quaternion and the attitude matrix
And (4) updating.
Optionally, the obtaining a coarse alignment result by solving the attitude matrix based on the bivector pose-determining triac algorithm and the recursive quaternion estimation REQUEST algorithm includes:
attitude transformation matrix from carrier inertial system to navigation inertial system based on TRIAD algorithm
Optimizing said process based on said REQUEST algorithm
Obtaining an optimal estimate of an attitude matrix
Optionally, the determination of the attitude transformation matrix from the carrier inertial system to the navigation inertial system based on the TRIAD algorithm
The method comprises the following steps:
based on attitude transformation matrix from navigation inertial system to navigation system
And attitude transformation matrix from carrier system to carrier inertial system
Acquiring the projections of the gravity acceleration under the navigation inertial system and the carrier inertial system at the current moment;
selecting different moments to carry out integral operation on the acceleration vector to respectively obtain the projections of the velocity vector under a navigation inertial system and a carrier inertial system;
determining the attitude transformation matrix according to the TRIAD principle and the projection of the velocity vector under the navigation inertial system and the carrier inertial system
Optionally, the current time tkThe projection of the lower gravitational acceleration on the navigation inertial system and the carrier inertial system is represented by the following formula:
wherein the projection g of the gravitational acceleration under the navigation systemn＝[0 0 -g]Projection g of gravitational acceleration on a carrier systembAvailable accelerometer output
Represents;
accordingly, at different times t1 and t2The projection of the velocity vector under the navigation inertial system and the carrier inertial system is represented by the following equation:
the attitude transformation matrix
Represented by the formula:
optionally, said optimizing said REQUEST algorithm based on said REQUEST algorithm
Obtaining an optimal estimate of an attitude matrix
The method comprises the following steps:
selecting integral of specific force as observation vector at tkThe time, the observation information is represented by the following formula:
initializing initial value of parameter, setting m0＝0，K0＝04×4，
At tkTime of day, calculated using local latitude L and alignment time t
Using gyro output angular rate
Computing
Solving t according to a calculation formula of observation informationkThe current incremental matrix delta K of the matrix K is obtained by the observation vector of the momentk，ΔKkRepresented by the formula:
zk＝bk×rk；
σk＝tr(Bk)；
selecting proper weight coefficient according to the influence of different observation vectors on the K matrix, and updating tkThe updating mode of the K matrix at the moment is as follows:
mk＝mk-1+αk
wherein ,αkThe same weight coefficient is adopted for each observation vector as the weight coefficient;
solving the eigenvector corresponding to the K maximum eigenvalue, and updating the attitude matrix estimated value
Judging whether the alignment time is reached;
if the alignment is not over, said at t againkTime of day, calculated using local latitude L and alignment time t
Using gyro output angular rate
Computing
A step (2);
if the alignment is finished, outputting the current attitude matrix estimated value
Optionally, the step of establishing a kalman filter error model by using the coarse alignment result obtained in the coarse alignment stage as an initial value, and performing iterative filtering alignment by using inertial device data stored at a past time to obtain the initial alignment result includes:
selecting an attitude misalignment angle of a systematic error
Speed error δ vnZero bias epsilon of gyrobAccelerometer zero offset
As the state quantity, a 12-dimensional system state equation is established:
wherein the 12-dimensional state quantities are:
the state transition matrix known from the state quantities is:
the system noise is:
wherein ,
gyroscope angular rate noise and accelerometer specific force noise respectively;
when the carrier is static, the navigation solves the speed, namely the system speed error. And (3) establishing a system observation equation by taking the speed error as an observed quantity:
Z＝HX+V
wherein the observation matrix H ═ 03×3 I3×3 03×3 03×3]The observation noise is a speed measurement noise V ═ VE VNVU]。
Optionally, the step of establishing a kalman filter error model by using the coarse alignment result obtained in the coarse alignment stage as an initial value, and performing iterative filtering alignment by using inertial device data stored at a past time to obtain the initial alignment result includes:
in the stage of storing filter alignment, 5 groups of stored inertial device data are sequentially read each time by resolving;
iterative filtering alignment is carried out by utilizing the gyro angle increment and the accelerometer specific force increment data at the past moment;
when the stored inertial device data are completely processed, continuously reading the inertial device data updated in real time;
and carrying out real-time filtering alignment by using the angular increment and specific force increment data at the current moment.
Optionally, the method further comprises:
the shaking environment is constructed such that the shaking environment simulates an actual shaking scene.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and together with the description, serve to explain the principles of the invention.
FIG. 1 is a flow chart of an inertial measurement unit alignment method provided by one embodiment of the present invention;
FIG. 2 is a flow chart of a coarse alignment REQUEST algorithm provided by one embodiment of the present invention;
FIG. 3 is a schematic diagram of alignment time allocation provided by one embodiment of the present invention;
FIG. 4 is a graph of test output data of an inertial measurement unit in a sloshing environment according to an embodiment of the present invention;
FIG. 5 is a diagram of data alignment results for a wobble base according to an embodiment of the invention.
Detailed Description
Reference will now be made in detail to the exemplary embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, like numbers in different drawings represent the same or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the invention, as detailed in the appended claims.
The embodiment of the application provides an inertial measurement unit alignment method, as shown in fig. 1, the method at least includes the following steps:
Before this step, the shaking environment needs to be constructed, so that the shaking environment simulates an actual shaking scene.
In one example, the inertia measurement assembly is mounted on a test vehicle, the engine is kept in a starting state, and people get on the vehicle to form a shaking interference environment. The inertia measurement assembly was connected to a regulated dc power supply and a test computer using a test cable, setting a 24V dc supply. After the test preparation is completed, the inertia measurement combination is powered on, the test computer navigation software is started, and the measurement output data of the triaxial fiber-optic gyroscope and the triaxial accelerometer are received and recorded in real time.
According to the above experimental contents, 5 minutes of inertial device data were continuously collected. After the acquisition is completed, the vehicle position is adjusted, and multiple groups of tests are repeated under the same test conditions. The inertial device test output data under the rocking base is shown in fig. 5. As can be seen from FIG. 5, the gyroscope and accelerometer output have large-amplitude shaking interference at each moment, and the inertial device error directly causes a large alignment error, so that an effective attitude initial value cannot be obtained.
And 102, decomposing the attitude matrix based on the inertial solidification principle.
Double-vector pose determination (TRIAD) is a process of solving a pose transformation matrix between two coordinate systems by observing the projection of two non-collinear vectors in different coordinate systems. The vector in the dual-vector attitude determination method is a determination vector, so that the method is only suitable for acquiring a constant attitude matrix. Under the swinging or shaking environment, the carrier attitude matrix can change along with the time, and effective earth rotation information is submerged by a larger interference angular rate, so that the double-vector attitude determination method is not completely applicable any more. Based on this, the inertia solidification principle-based decomposition attitude matrix is represented by the following formula:
wherein n represents a navigation coordinate system, i.e. a local geographical coordinate system; b represents a carrier coordinate system which is fixedly connected with the carrier;
the navigation inertial coordinate system is a coordinate system which is determined according to the inertial solidification principle by aiming at the navigation coordinate system at the initial moment;
the inertial coordinate system of the carrier is expressed and is determined according to the inertial solidification principle by aligning the carrier coordinate system at the initial moment;
representing a posture conversion matrix from a navigation inertial system to a navigation system, changing along with time, and acquiring and updating through alignment time and the resolved position information;
representing a posture conversion matrix from a carrier system to a carrier inertial system, changing along with time, and acquiring and updating through gyroscope output angular rate information;
the attitude transformation matrix representing the system from the carrier inertia system to the navigation inertia system is a constant matrix corresponding to the alignment start time.
When the carrier position is not moved, the navigation system rotates along with the rotation of the earth,
only with the local latitude L and the earth's rotation angle omega at the current timeiet is related. Based thereon, wherein the attitude matrix
The decomposition is as follows:
in the formula ,
indicating the initial moment of alignment t0The earth coordinate system is a coordinate system determined according to the inertial coagulation principle.
From the above, the attitude matrix is determined
Is to solve for
Because the earth rotation information under the shaking interference is no longer effective, the gravity acceleration vectors at two moments can be selected and respectively observed in the navigation inertial system
And carrier inertia system
Indirectly using the dual-vector attitude determination principle to obtain
And 103, solving the attitude matrix based on a double-vector attitude determination TRIAD algorithm and a recursive quaternion estimation REQUEST algorithm to obtain a coarse alignment result.
The traditional inertial system rough alignment method only utilizes acceleration observation information at different moments, and the solving precision is limited by sudden change interference at the selected moment. Therefore, how to effectively utilize the measurement information and eliminate the sudden interference at different moments is to solve
A significant concern is required. Based on the coarse alignment scheme, the coarse alignment scheme based on the TRIAD and REQUEST algorithms is designed, and the coarse alignment scheme is determined based on the TRIAD principle in the early stage of the coarse alignment stage
At the later stage of the coarse alignment stage, REQUEST algorithm optimization is applied
Obtaining an optimal estimate of an attitude matrix
Specifically, the method for solving the attitude matrix based on the dual-vector attitude determination TRIAD algorithm and the recursive quaternion estimation REQUEST algorithm to obtain a coarse alignment result includes: attitude transformation matrix from carrier inertial system to navigation inertial system based on TRIAD algorithm
Optimizing said process based on said REQUEST algorithm
Obtaining an optimal estimate of an attitude matrix
Determining an attitude transformation matrix from a carrier inertial system to a navigation inertial system based on a TRIAD algorithm
The method comprises the following steps:
first, a matrix is transformed according to the attitude from the navigation inertial system to the navigation system
And attitude transformation matrix from carrier system to carrier inertial system
Acquiring the projections of the gravity acceleration under the navigation inertial system and the carrier inertial system at the current moment; at the current time tkFor example, it is specifically represented by the following formula:
wherein the projection g of the gravitational acceleration under the navigation systemn＝[0 0 -g]Projection g of gravitational acceleration on a carrier systembAvailable accelerometer output
And (4) showing.
Secondly, large alignment errors can be caused by periodic interference acceleration under a shaking environment, and in order to reduce the influence of interference, integral operation is carried out on acceleration vectors at different moments to respectively obtain the projections of the velocity vectors under a navigation inertial system and a carrier inertial system; at different times t1 and t2The following is specifically represented by the following formula:
and finally, determining the attitude transformation matrix according to the TRIAD principle and the projection of the velocity vector under the navigation inertial system and the carrier inertial system
In particular, the attitude transformation matrix
Represented by the formula:
the meaning of the REQUEST algorithm is recursive quaternion estimation, the method is derived from a batch processing algorithm, and the principle is that quaternion quantization attitude matrix parameters are utilized to convert a quaternion updating problem into a matrix characteristic value solving problem. The REQUEST algorithm can be effectively applied to parameter estimation under the condition of more observation vectors, and the key point of applying the REQUEST algorithm is to recursively solve a four-dimensional matrix K.
The process of applying the recursive solution of the REQUEST algorithm, based on which the optimization is performed, is illustrated with reference to FIG. 2
Obtaining an optimal estimate of an attitude matrix
The method comprises the following steps:
zk＝bk×rk；
σk＝tr(Bk)；
mk＝mk-1+αk
wherein ,αkThe same weight coefficient is adopted for each observation vector as the weight coefficient;
And 104, establishing a Kalman filtering error model by taking the coarse alignment result obtained in the coarse alignment stage as an initial value, and performing iterative filtering alignment by using inertial device data stored at the past moment to obtain the initial alignment result.
The method comprises the following steps of establishing a Kalman filtering error model by taking the coarse alignment result obtained in the coarse alignment stage as an initial value, and carrying out iterative filtering alignment by using inertial device data stored at the past moment to obtain the initial alignment result, wherein the method comprises the following steps: in the stage of storing filter alignment, 5 groups of stored inertial device data are sequentially read each time by resolving; iterative filtering alignment is carried out by utilizing the gyro angle increment and the accelerometer specific force increment data at the past moment; when the stored inertial device data are completely processed, continuously reading the inertial device data updated in real time; and carrying out real-time filtering alignment by using the angular increment and specific force increment data at the current moment.
Specifically, after the coarse alignment stage of step 103, the attitude matrix is obtained preliminarily. Because the current alignment result still has an attitude misalignment angle, the attitude angle error needs to be further corrected by using a fine alignment process. Selecting an attitude misalignment angle of a systematic error
Speed error δ vnZero bias epsilon of gyrobAccelerometer zero offset
As the state quantity, a 12-dimensional system state equation is established:
wherein the 12-dimensional state quantities are:
the state transition matrix known from the state quantities is:
the system noise is:
wherein ,
gyroscope angular rate noise and accelerometer specific force noise respectively;
when the carrier is static, the navigation solves the speed, namely the system speed error. And (3) establishing a system observation equation by taking the speed error as an observed quantity:
Z＝HX+V
wherein the observation matrix H ═ 03×3 I3×3 03×3 03×3]The observation noise is a speed measurement noise V ═ VE VNVU]。
And in the storage filtering alignment stage, multiple groups of inertial device data can be processed by resolving each time, compared with real-time filtering, more times of filtering resolving are completed in the same time, and the alignment precision is improved by increasing the alignment times. The storage filtering alignment time is determined by the coarse alignment time, is only one fifth of the coarse alignment time, and the accuracy of the alignment result is ensured while the alignment time is compressed.
And 105, outputting the initial alignment result in the shaking environment.
Assuming the geographical coordinates of the location of the binding test: latitude 39.8122 °, longitude 116.1515 °, height 60 m. The total initial alignment time is set to 270 seconds and the inertial system coarse alignment time is set to 210 seconds. The memory filter alignment time determined by the coarse alignment time is 42 seconds and the remaining period is the real-time filter alignment. The alignment time allocation map is shown in fig. 3. After the configuration of each parameter is completed, the inertial device test data (as shown in fig. 4) collected in step 101 is input into the alignment algorithm described in step 102-104, and the optimal estimation of the attitude matrix can be obtained by applying the coarse alignment of the triac/REQUEST algorithm and the memory card elman filter fine alignment process, and the initial alignment result of the system in the shaking environment is output. The initial alignment results using the method of the present invention are shown in fig. 5. The data of other groups of inertial devices under the same test conditions are input into an alignment algorithm, and the north-seeking repeatability of the data of the groups is less than 0.1 degrees, as shown in table 1.
Table 1:
| index (I) | Alignment time(s) | Course angle (°) |
| |
269.8199 | 88.8436 |
| |
269.9399 | 88.8255 |
| Group 3 | 269.7399 | 88.8511 |
| Group 4 | 269.7799 | 88.8301 |
| Group 5 | 269.7899 | 88.8546 |
| Group 6 | 269.7399 | 88.8436 |
| Repeatability of | —— | 0.035 |
In summary, the inertial measurement unit alignment method provided by the embodiment of the present application acquires output data of an inertial device in a shaking environment; decomposing an attitude matrix based on an inertial solidification principle; solving an attitude matrix based on a double-vector attitude determination TRIAD algorithm and a recursion quaternion estimation REQUEST algorithm to obtain a coarse alignment result; establishing a Kalman filtering error model by taking a coarse alignment result obtained in a coarse alignment stage as an initial value, and performing iterative filtering alignment by using inertial device data stored at the past moment to obtain an initial alignment result; outputting an initial alignment result in a shaking environment; the problem that the alignment precision of the traditional coarse alignment method is low under the condition of large-amplitude shaking interference in the related technology can be solved; according to the initial alignment result of the vehicle-mounted positioning and orientation system under the shaking base, the method can be effectively suitable for the strong shaking interference environment, and the optimal alignment precision is realized while the alignment time is shortened.
Meanwhile, an attitude matrix to be solved is determined based on double-vector attitude determination, and the attitude matrix is estimated and optimized based on recursion quaternion, so that the anti-interference capability of a coarse alignment algorithm is improved. Meanwhile, an iterative filtering fine alignment scheme is designed by innovatively using data of a storage inertia device, posture correction is completed based on inertia group data at the past moment, and reasonable balance of alignment time and alignment precision is realized.
Other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention following, in general, the principles of the invention and including such departures from the present disclosure as come within known or customary practice within the art to which the invention pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims.
It will be understood that the invention is not limited to the precise arrangements described above and shown in the drawings and that various modifications and changes may be made without departing from the scope thereof. The scope of the invention is limited only by the appended claims.
Claims (10)
1. An inertial measurement unit alignment method, comprising:
acquiring output data of an inertial device in a shaking environment;
decomposing an attitude matrix based on an inertial solidification principle;
solving the attitude matrix based on a double-vector attitude determination TRIAD algorithm and a recursion quaternion estimation REQUEST algorithm to obtain a coarse alignment result;
establishing a Kalman filtering error model by taking the coarse alignment result obtained in the coarse alignment stage as an initial value, and carrying out iterative filtering alignment by using inertial device data stored at the past moment to obtain an initial alignment result;
outputting the initial alignment result in the shaking environment.
2. The method of claim 1, wherein the principal of inertial coagulation-based decomposition of the attitude matrix is represented by:
wherein n represents a navigation coordinate system, i.e. a local geographical coordinate system; b represents a carrier coordinate system which is fixedly connected with the carrier;
the navigation inertial coordinate system is a coordinate system which is determined according to the inertial solidification principle by aiming at the navigation coordinate system at the initial moment;
the inertial coordinate system of the carrier is expressed and is determined according to the inertial solidification principle by aligning the carrier coordinate system at the initial moment;
representing a slaveChanging the attitude transformation matrix from the navigation inertial system to the navigation system along with time, and acquiring and updating through alignment time and the resolved position information;
representing a posture conversion matrix from a carrier system to a carrier inertial system, changing along with time, and acquiring and updating through gyroscope output angular rate information;
the attitude transformation matrix representing the inertial system of the carrier to the inertial system of the navigation is a constant value matrix corresponding to the alignment starting moment;
wherein the attitude matrix
The decomposition is as follows:
in the formula ,
indicating the initial moment of alignment t0The earth coordinate system is a coordinate system determined according to the inertial coagulation principle.
3. The method of claim 2, wherein the step of generating the second signal comprises generating a second signal based on the first signal and the second signal
The solving process comprises the following steps:
using the angular velocity of the gyroscope
Projection of alternative rotation angular rates onto a carrier system
From the alignment start time, the quaternion is resolved and updated in each sampling interval;
completing the attitude matrix according to the conversion relation between the quaternion and the attitude matrix
And (4) updating.
4. The method of claim 2, wherein solving the pose matrix based on a bivector pose-determining TRIAD algorithm and a recursive quaternion estimation REQUEST algorithm to obtain a coarse alignment result comprises:
attitude transformation matrix from carrier inertial system to navigation inertial system based on TRIAD algorithm
Optimizing said process based on said REQUEST algorithm
Obtaining an optimal estimate of an attitude matrix
5. Method according to claim 4, characterized in that said determination of the attitude transformation matrix from the carrier inertial system to the navigation inertial system based on the TRIAD algorithm is carried out
The method comprises the following steps:
based on attitude transformation matrix from navigation inertial system to navigation system
And attitude transformation matrix from carrier system to carrier inertial system
Acquiring the projections of the gravity acceleration under the navigation inertial system and the carrier inertial system at the current moment;
selecting different moments to carry out integral operation on the acceleration vector to respectively obtain the projections of the velocity vector under a navigation inertial system and a carrier inertial system;
determining the attitude transformation matrix according to the TRIAD principle and the projection of the velocity vector under the navigation inertial system and the carrier inertial system
6. The method of claim 5,
the current time tkThe projection of the lower gravitational acceleration on the navigation inertial system and the carrier inertial system is represented by the following formula:
wherein the projection g of the gravitational acceleration under the navigation systemn＝[0 0 -g]The projection g of the gravity acceleration under the carrier system can be output by an accelerometer
Represents;
accordingly, at different times t1 and t2The projection of the velocity vector under the navigation inertial system and the carrier inertial system is represented by the following equation:
the attitude transformation matrix
Represented by the formula:
7. the method according to claim 2, wherein said optimizing said REQUEST algorithm based on said REQUEST algorithm
Obtaining an optimal estimate of an attitude matrix
The method comprises the following steps:
selecting integral of specific force as observation vector at tkThe time, the observation information is represented by the following formula:
initializing initial value of parameter, setting m0＝0，K0＝04×4，
At tkTime of day, calculated using local latitude L and alignment time t
Using gyro output angular rate
Computing
Solving t according to a calculation formula of observation informationkThe current incremental matrix delta K of the matrix K is obtained by the observation vector of the momentk，ΔKkRepresented by the formula:
zk＝bk×rk；
σk＝tr(Bk)；
selecting proper weight coefficient according to the influence of different observation vectors on the K matrix, and updating tkK matrix of time of day, updateThe method is as follows:
mk＝mk-1+αk
wherein ,αkThe same weight coefficient is adopted for each observation vector as the weight coefficient;
solving the eigenvector corresponding to the K maximum eigenvalue, and updating the attitude matrix estimated value
Judging whether the alignment time is reached;
if the alignment is not over, said at t againkTime of day, calculated using local latitude L and alignment time t
Using gyro output angular rate
Computing
A step (2);
if the alignment is finished, outputting the current attitude matrix estimated value
8. The method according to claim 1, wherein the establishing a kalman filter error model with the coarse alignment result obtained in the coarse alignment stage as an initial value, and performing iterative filtering alignment using inertial device data stored at a past time to obtain the initial alignment result comprises:
selecting an attitude misalignment angle of a systematic error
Speed error δ vnZero bias epsilon of gyrobZero bias of accelerometerbAs the state quantity, a 12-dimensional system state equation is established:
wherein the 12-dimensional state quantities are:
the state transition matrix known from the state quantities is:
the system noise is:
wherein ,
gyroscope angular rate noise and accelerometer specific force noise respectively;
when the carrier is static, the navigation solves the speed, namely the system speed error. And (3) establishing a system observation equation by taking the speed error as an observed quantity:
Z＝HX+V
wherein the observation matrix H ═ 03×3 I3×3 03×3 03×3]The observation noise is a speed measurement noise V ═ VE VN VU]。
9. The method according to claim 1, wherein the establishing a kalman filter error model with the coarse alignment result obtained in the coarse alignment stage as an initial value, and performing iterative filtering alignment using inertial device data stored at a past time to obtain the initial alignment result comprises:
in the stage of storing filter alignment, 5 groups of stored inertial device data are sequentially read each time by resolving;
iterative filtering alignment is carried out by utilizing the gyro angle increment and the accelerometer specific force increment data at the past moment;
when the stored inertial device data are completely processed, continuously reading the inertial device data updated in real time;
and carrying out real-time filtering alignment by using the angular increment and specific force increment data at the current moment.
10. The method of claim 1, further comprising:
the shaking environment is constructed such that the shaking environment simulates an actual shaking scene.
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