CN117073719B - Relay type rapid air alignment method - Google Patents

Relay type rapid air alignment method Download PDF

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CN117073719B
CN117073719B CN202310968340.2A CN202310968340A CN117073719B CN 117073719 B CN117073719 B CN 117073719B CN 202310968340 A CN202310968340 A CN 202310968340A CN 117073719 B CN117073719 B CN 117073719B
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汪进文
薄煜明
朱建良
吴盘龙
付梦印
吴祥
何山
王超尘
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Nanjing University of Science and Technology
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    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
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    • G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices
    • G—PHYSICS
    • G01—MEASURING; TESTING
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Abstract

The invention provides a relay type rapid air alignment method which mainly comprises an optimization stage and a filtering stage, wherein an initial attitude angle is used as an optimization object to construct an optimization model, and a K matrix is used as a state variable to construct a filtering model; then designing an internal connection force mode of an optimization stage and an external connection force mode of transition from the optimization stage to a filtering stage, and playing the characteristic of rapidness of an optimization algorithm in a self-adaptive multi-constraint mode so as to accelerate an alignment process; the filtering stage is taken as a main body to exert the high-precision characteristic of the filtering algorithm, and the alignment precision is improved.

Description

Relay type rapid air alignment method
Technical Field
The invention belongs to the field of acquisition of initial gestures of inertial navigation in an unknown complex environment, and particularly relates to a relay type rapid air alignment method.
Background
The aerial alignment of the shell refers to a process of determining the initial attitude of a strapdown inertial navigation system (Strap-down inertial navigation system, SINS) in the flight of the shell, and the core of the process is to determine an initial attitude matrix between a shell coordinate system and a reference navigation coordinate system. The air alignment technology of the guided projectile directly relates to the navigation precision and the starting time of the SINS, so that the air alignment technology is always a research key point and a difficult point in the field of inertial navigation of the projectile. In the flight phase of the brake shell, the micro inertial navigation air alignment faces the challenges of high complexity such as satellite interference, random wind interference and the like, high speed, high rotation, high overload and the like, so that the research on the micro inertial navigation air alignment method under the high-complexity and high-dynamic environment needs to be conducted deeply.
Generally, the initial alignment is accomplished in two successive stages: coarse alignment and fine alignment. Coarse alignment only coarsely determines the pose matrix, but has the advantage of being fast. Accurate alignment can obtain an accurate pose matrix, but has the disadvantage of long convergence time. Many attitude estimation methods based on SINS and Global navigation satellite System (Global Navigation Satellite System, GNSS) information have been proposed for certain specific applications. However, these attitude estimation methods are not suitable for the in-flight alignment of shells of GNSS assisted SINS in high dynamic environments. The method combines the advantages of coarse alignment and fine alignment, and can adopt a dynamic coarse alignment method to rapidly determine an initial attitude matrix in the process of flying the shell. For dynamic coarse alignment methods Wu proposes optimization-based alignment methods (OBA). The OBA method is derived based on a gesture matrix decomposition technology, and the method decomposes a required gesture matrix into two time-varying gesture matrixes and a steady gesture matrix, and directly calculates the time-varying gesture matrixes by using a gesture update program. To obtain a steady state matrix, the problem can be converted into a Wahba problem by constructing a vector observation. In 1965 Wahba first proposed a method for determining the pose of vector observations, indicating that the optimal pose matrix minimizes the loss function. There are two methods for solving the Wahba problem. One is a deterministic algorithm such as SVD, fast linear pose estimator (Fast LinearAttitude Estimator, FLAE) and quaternion estimator (Quaternion Estimator, QUEST). The other is a random algorithm such as Recursive REQUEST (REQUEST), optimal REQUEST (OPREQ) and matrix Kalman filter (Matrix Kalman filter, MKF). Although these methods can effectively solve the problem of inertial navigation initial alignment in the conventional scenario, the contradiction between the initial alignment precision and the alignment time still cannot be solved, the coarse alignment is to trade off the precision for a short time, and the precise alignment is to trade off the time for a high precision, so that in the high-complexity and high-dynamic environments, how to effectively balance the alignment precision and the alignment time becomes a problem to be solved.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a relay type rapid air alignment method, which combines the rapidity of an optimization algorithm and the high accuracy of a filtering algorithm, has complementary advantages, effectively solves the problem of contradiction between alignment accuracy and alignment time, and comprehensively improves the air alignment performance of the guided shell.
The technical scheme adopted by the invention is as follows: a relay type rapid aerial alignment method comprises the steps of firstly constructing an optimization model of an optimization stage by taking an initial attitude angle as an optimization object, and reconstructing a filtering model of a filtering stage based on the optimal initial attitude angle obtained in the optimization stage; and then, based on an internal connection force mode of the self-adaptive multi-constraint mode design optimization stage and an external connection force mode of transition from the optimization stage to the filtering stage, determining an initial gesture so as to realize alignment.
Further, the optimization stage takes an optimization model as a fitness function, and adopts an intelligent optimization algorithm and a sliding window form for optimization.
Further, the optimization model is:
in (θ) 0 ,γ 0 ,ψ 0 ) Representing an initial attitude angle; i represent the 2-norm of the two-dimensional model, gesture matrix
，And->At t k Observation vector of time.
Further, the inscription force mode of the design optimization stage comprises:
sliding window based optimization model determination J k By delta A k ＝A max J k rand determination δA k Through A k 、δA k Determining the upper bound UB of the initial population of the intelligent optimization algorithm k+1 And infinitesimal LB k+1 The method comprises the steps of carrying out a first treatment on the surface of the Wherein A is max Represents the initial attitude maximum, rand represents [0,1 ]]Random numbers obeying uniform distribution among them, A k Representing the optimal initial attitude, delta A, acquired in the sliding window at the moment k k Representing a controllable range;
if UB is an upper bound k+1 ＞A max Then another UB k+1 ＝A max The method comprises the steps of carrying out a first treatment on the surface of the If the infinitesimal LB k+1 ＜A min Then another LB k+1 ＝A min ，A min Representing an initial pose minimum.
Further, the external force mode for the transition from the optimization stage to the filtering stage specifically includes:
determining a relay function for transition from the optimization stage to the filtering stage according to the loss duty ratio;
if the relay function is larger than the relay threshold value, the optimal initial attitude angle obtained in the optimization stage is obtainedConversion to quaternion->Form, according to quaternion->Determining an initial state matrix X of a filter model 0 And (5) finishing external relay, otherwise, continuing optimizing through an optimizing stage.
Further, the constructing a filtering model of the filtering stage includes:
according to t k Time observation vectorAnd->Calculate matrix +.>
In the method, in the process of the invention,
according to the matrixThe feature vector corresponding to the maximum feature value can obtain the initial gesture matrix +.>Obtaining K k The state equation of the matrix is: k (K) k ＝K k-1 ；
Order state estimation matrix X k ＝K k The observed quantity matrix isThe method for establishing the shell air alignment filtering model comprises the following steps:
in the formula, the matrix f=i 4 ，H＝I 4 Wherein I 4 Is a matrix of cells, W k And V k System noise and measurement noise, respectively, and is fullFoot:
where vec () is a vectorization operator, q k R is the mean value of system noise k To measure the noise mean, Q k R is the mean square error of system noise k The noise mean square error is measured for the system.
Further, the relay function is:
wherein p is k To loss the duty cycle.
Further, the relay threshold is 10.
Compared with the prior art, the invention has the beneficial effects that:
(1) The method mainly comprises an optimization stage and a filtering stage, wherein an initial attitude angle is used as an optimization object to construct an optimization model, and a K matrix is used as a state variable to construct a filtering model; then designing an internal connection force mode of an optimization stage and an external connection force mode of transition from the optimization stage to a filtering stage, and playing the characteristic of rapidness of an optimization algorithm in a self-adaptive multi-constraint mode so as to accelerate an alignment process; the filtering stage is taken as a main body to exert the high-precision characteristic of the filtering algorithm, so that the alignment precision is improved;
(2) In the method, constraint of an internal stress stage designs an optimization algorithm in a next sliding window to generate upper and lower definitive bounds of an initial population according to a loss function value in the current sliding window, so that a search range is limited, and the optimization algorithm can quickly and accurately search an optimal initial attitude angle; the constraint of the external relay stage is to design a relay function according to the loss ratio so as to determine the time for transition from the optimization stage to the filtering stage, and convert the optimal initial attitude angle obtained in the optimization stage into a K matrix form, and use the K matrix form as the initial value of the state of the filtering stage so as to improve the rapidity and the high precision of the filtering algorithm.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a schematic diagram of the optimization stage.
Fig. 3 is a view of a projectile relay type aerial alignment frame.
Detailed Description
The following is a detailed description of the implementation of the present invention with reference to the accompanying drawings.
The aerial alignment is the basis of realizing accurate navigation by a Strapdown Inertial Navigation System (SINS) of the guided projectile, and the micro inertial navigation aerial alignment of the guided projectile faces the challenges of high complexity such as satellite interference, random wind disturbance and the like, high speed, high rotation, high overload and the like, and the like; then designing an internal connection force mode of an optimization stage and an external connection force mode of transition from the optimization stage to a filtering stage, and playing the characteristic of rapidness of an optimization algorithm in a self-adaptive multi-constraint mode so as to accelerate an alignment process; the method mainly comprises the steps of taking a filtering stage as a main body to exert the high-precision characteristic of a filtering algorithm and improve the alignment precision, wherein the constraint of an internal relay stage mainly designs an upper and lower definitive of an initial population generated by an optimization algorithm in a next sliding window according to a loss function value in the current sliding window so as to limit a search range, so that the optimization algorithm can quickly and accurately search an optimal initial attitude angle, the constraint of an external force stage is to design a relay function according to a loss ratio so as to determine the time for transition from the optimization stage to the filtering stage, and the optimal initial attitude angle obtained in the optimization stage is converted into a K matrix form and is used as a state initial value of the filtering stage so as to improve the rapidity and the high precision of the filtering algorithm, and the method is described in detail.
A key problem with the aerial alignment of projectiles is determining the pose matrix from the projectile coordinate system to the navigational coordinate systemThe initial alignment problem of GNSS assisted SINS during the projectile flight is mainly studied, and the alignment process is time-to-timeAnd 0 starts in between.
According to the chain law, a gesture matrixCan be decomposed into:
in the formula, the navigation coordinate system at the time t is n (t), and the projectile coordinate system is b (t). The navigation coordinate system at time 0 is n (0), and the bullet coordinate system is b (0).
According to the velocity differential equation of SINS:
in the method, in the process of the invention,R e for the average radius of the earth, ω ie Is the rotation angular velocity of the earth, [ Lλh ]] T For the position, respectively representing latitude, longitude and altitude,/->The east, north and sky speeds are indicated as speeds, respectively. f (f) b Triaxial specific force, g, measured for accelerometer n Is the local gravitational acceleration.
Because the shell flight time is short and the falling point distance is short, the navigation coordinate system n can be considered to be unchanged, and then:
and (3) combining the formula (2) and the formula (3), and integrating two sides of the equation simultaneously to obtain the following components:
in the method, in the process of the invention,can be obtained by a rotation vector method.
The simplified formula (4) can be obtained:
in the method, in the process of the invention,
and->The specific recursive solution is as follows:
the solution to equation (5) is the Wahba problem. Converting it into an optimization problem, then an fitness function can be constructed as:
in (θ) 0 ,γ 0 ,ψ 0 ) Representing an initial attitude angle; i represent 2-norm.
Equation (7) is an air alignment optimization model, and in theory, J (theta) 0 ,γ 0 ,ψ 0 ) =0, but since the equation is an transcendental equation, it cannot be solved directly,the optimal initial pose needs to be found to satisfy equation (7). Therefore, the equation (7) can be used as a fitness function, the initial attitude angle is used as an optimizing object, and the intelligent optimizing algorithm is adopted to realize the air alignment.
According to t k Time observation vectorAnd->Calculation of +.>Matrix:
in the method, in the process of the invention,
according toThe initial posture matrix can be obtained by the feature vector corresponding to the maximum feature value of the matrix>Theoretically, a +.>Should be constant, therefore, K k The state equation of the matrix is:
K k ＝K k-1 (9)
according to equations (8) and (9), the order state estimation matrix X k ＝K k The observed quantity matrix isCan establish shell air alignment filtering model：
Wherein F=I 4 ，H＝I 4 ，I 4 Is a matrix of cells. W (W) k And V k System noise and measurement noise, respectively, and satisfy:
where vec () is a vectorization operator.
Equation (10) can be solved by adopting MKF to obtain the optimal K k And extracting an initial attitude angle by the matrix to realize an alignment process.
The relay type aerial alignment is mainly divided into an optimization stage and a filtering stage, wherein the relay type aerial alignment is mainly divided into an internal connection force mode of the optimization stage and an external connection force mode of transition from the optimization stage to the filtering stage.
In the optimizing stage, the sliding window is adopted for optimizing, on one hand, the optimizing times of an optimizing algorithm are reduced, the speed of the optimizing stage is increased, and on the other hand, the influence of noise on an optimizing result can be reduced in the sliding window mode. For this purpose, formula (7) is modified as:
where N represents the sliding window length.
Referring to fig. 2, the internal contact force mode mainly occurs between two sliding windows, taking k time as an example, an intelligent optimizing algorithm is adopted to obtain an optimal initial posture a in the k time sliding window k Will A k Transmitting to the k+1 moment, providing a range reference for generating an initial population by the intelligent optimizing algorithm in the sliding window of the k+1 moment, namely
In the formula UB k+1 Upper definition of initial population of intelligent optimization algorithm in k+1 moment sliding window is represented, LB k+1 The lower definition of the initial population of the intelligent optimizing algorithm in the sliding window at the moment k+1 is represented, A k Representing the optimal initial attitude, delta A, acquired in the sliding window at the moment k k Representing a controllable range.
As can be seen from fig. 2, the optimal initial pose obtained in each sliding window is gradually relayed, and the accuracy of the initial pose directly determines the magnitude of the loss function (12). When the obtained value of the loss function in the current sliding window is larger, the obtained initial posture error is larger, and when the initial population is generated in the next sliding window, the range of the upper and lower bounds needs to be enlarged, namely delta A is enlarged k The method comprises the steps of carrying out a first treatment on the surface of the When the value of the loss function obtained in the current sliding window is smaller, the obtained initial posture error is smaller, and when the initial population is generated in the next sliding window, the range of upper and lower bounds can be narrowed, namely delta A is reduced k . Thus, δA can be constructed k And J k Linear relationship between, i.e
δA k ＝A max J k rand (14)
Wherein A is max Representing an initial pose maximum, i.e., a search maximum; rand represents [0,1 ]]Random numbers subject to uniform distribution.
The specific flow of the internal relay mode is as follows:
the optimization stage adopts an intelligent optimizing algorithm to quickly lock to the vicinity of the real initial attitude, and the filtering stage adopts an MKF algorithm to slowly estimate the real initial attitude, so that the moment of transition from the optimization stage to the filtering stage is important. Obtaining heuristics from the information entropy, and defining loss ratio as follows:
as can be seen from equation (15), as the sliding window moves, p k The loss calculated by the current loss function is the proportion of the historical loss, and the filtering stage can be relayed when the proportion is reduced to a certain degree. For convenience of description, logarithms are taken on both sides of the formula (15), and a relay function is obtained:
wherein Hp is k The moment of transition from the optimization stage to the filtering stage is mainly discriminated as a relay function. The Hp is set up herein k When the pressure is more than or equal to 10, the relay is opened, and at the moment, p k ≤10 -10 。
The optimization stage can obtain rough optimal initial attitude angleThe filtering stage is K k The matrix is used as the quantity to be estimated, for which purpose +.>Conversion to K k A matrix. There is another form for formula (12), namely
Wherein q represents a posture quaternion corresponding to the initial posture angle, q T q＝1。
From the formula (17), it can be seen that theoretically q T K k q=1, a specific solution K can be obtained k ＝qq T . Thus, the result of the optimization stageConversion to quaternion->It is possible to obtain a solution,
equation (18) is used as the initial state matrix of the filtering stage MKF, i.eThereby completing the external relay process. The external relay mode comprises the following specific procedures:
in summary, the shell relay type aerial alignment frame is shown in fig. 3, and the relay type aerial alignment frame is mainly divided into an optimizing stage and a filtering stage, and the relay type aerial alignment frame is mainly divided into an internal connection force mode of the optimizing stage and an external connection force mode of the optimizing stage to the filtering stage.
The optimization stage can adopt intelligent optimization algorithms such as particle swarm optimization algorithm, genetic algorithm and the like to perform initial attitude optimization.
The foregoing examples merely represent embodiments of the present application, which are described in more detail and are not to be construed as limiting the scope of the invention. It should be noted that it would be apparent to those skilled in the art that various modifications and improvements could be made without departing from the spirit of the present application, which would be within the scope of the present application. Accordingly, the scope of protection of the present application is to be determined by the claims appended hereto.

Claims (7)

1. A relay type rapid air alignment method is characterized in that an initial attitude angle is used as an optimization object to construct an optimization model of an optimization stage, and a filtering model of a filtering stage is reconstructed based on the optimal initial attitude angle obtained in the optimization stage; then, based on an internal connection force mode of the self-adaptive multi-constraint mode design optimization stage and an external connection force mode of transition from the optimization stage to the filtering stage, determining a final initial gesture so as to realize alignment;
the inscription force mode of the design optimization stage comprises the following steps:
sliding window based optimization model determination J k By delta A k ＝A max J k rand determination δA k Through A k 、δA k Determining the upper bound UB of the initial population of the intelligent optimization algorithm k+1 And infinitesimal LB k+1 The method comprises the steps of carrying out a first treatment on the surface of the Wherein A is max Represents the initial attitude maximum, rand represents [0,1 ]]Random numbers obeying uniform distribution among them, A k Representing the optimal initial attitude, delta A, acquired in the sliding window at the moment k k Representing a controllable range;
if UB is an upper bound k+1 ＞A max Then another UB k+1 ＝A max The method comprises the steps of carrying out a first treatment on the surface of the If the infinitesimal LB k+1 ＜A min Then another LB k+1 ＝A min ，A min Representing an initial pose minimum;
the external force mode for the transition from the optimization stage to the filtering stage specifically comprises the following steps:
determining a relay function for transition from the optimization stage to the filtering stage according to the loss duty ratio;
if the relay function is larger than the relay threshold value, the optimal initial attitude angle obtained in the optimization stage is obtainedConversion to quaternion->Form, according to quaternion->Obtaining an initial state matrix X of a filtering model 0 Finishing external relay, otherwise, continuing optimizing through an optimizing stage;
the relay function is as follows:
wherein p is k To loss the duty cycle.
2. A relay type rapid air alignment method as defined in claim 1, wherein the optimization model is:
in (θ) 0 ,γ 0 ,ψ 0 ) Representing an initial attitude angle; i represent the 2-norm of the two-dimensional model, gesture matrix
，
And->At t k Observation vector of time.
3. The relay type rapid air alignment method according to claim 2, wherein the optimization stage takes an optimization model as a fitness function, and adopts an intelligent optimization algorithm and a sliding window form for optimization.
4. A relay type rapid air alignment method according to claim 3, wherein the intelligent optimizing algorithm adopts a particle swarm optimizing algorithm or a genetic algorithm.
5. A relay type rapid air alignment method as claimed in claim 1, wherein said up-bound UB k+1 And infinitesimal LB k+1 The method comprises the following steps:
6. a relay type rapid air alignment method as defined in claim 5, wherein constructing the filtering model of the filtering stage comprises:
according to t k Time observation vectorAnd->Calculate matrix +.>
In the method, in the process of the invention,
matrix K k The state equation of (2) is: k (K) k ＝K k-1 ；
Order state estimation matrix X k ＝K k The observed quantity matrix isThe method for establishing the shell air alignment filtering model comprises the following steps:
in the formula, the matrix f=i 4 ，H＝I 4 Wherein I 4 Is a matrix of cells, W k And V k System noise and measurement noise, respectively, and satisfy:
where vec () is a vectorization operator, q k R is the mean value of system noise k To measure the noise mean, Q k R is the mean square error of system noise k The noise mean square error is measured for the system.
7. A relay type rapid air alignment method according to claim 1, wherein the relay threshold is 10.
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