CN117073719B - Relay type rapid air alignment method - Google Patents

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

A relay-type rapid aerial alignment method

Technical field

The invention belongs to the field of initial attitude acquisition of inertial navigation in unknown complex environments, and specifically relates to a relay-type rapid air alignment method.

Background technique

Aerial alignment of artillery shells refers to the process of determining the initial attitude of the strap-down inertial navigation system (SINS) during the flight of the artillery shell. The core of this process is to determine the initial attitude between the projectile coordinate system and the reference navigation coordinate system. matrix. The aerial alignment technology of guided artillery shells is directly related to the navigation accuracy and activation time of SINS, so it has always been a research focus and difficulty in the field of artillery inertial navigation. During the flight stage of guided projectiles, micro-inertial navigation aerial alignment faces challenges such as "high" complexity such as satellite interference and random wind disturbance, and "high" dynamics such as high speed, high rotation, and high overload. To this end, in-depth high-complexity research is required. and research on micro-inertial navigation aerial alignment methods in highly dynamic environments.

Generally speaking, initial alignment is accomplished in two consecutive stages: coarse alignment and fine alignment. Coarse alignment only roughly determines the attitude matrix, but has the advantage of being fast. Precision alignment can obtain an accurate attitude matrix, but it has the disadvantage of long convergence time. Many attitude estimation methods based on SINS and Global Navigation Satellite System (GNSS) information have been proposed for some special applications. However, these attitude estimation methods are not suitable for GNSS-assisted SINS artillery aerial alignment in highly dynamic environments. Combining the advantages of coarse alignment and fine alignment, the dynamic coarse alignment method can be used to quickly determine the initial attitude matrix during the flight of the projectile. For the dynamic coarse alignment method, Wu proposed the optimization-based alignment method (optimization-basedAlignment, OBA). The OBA method is derived based on the attitude matrix decomposition technology. This method decomposes the required attitude matrix into two time-varying attitude matrices and a steady attitude matrix, and uses the attitude update program to directly calculate the time-varying attitude matrix. In order to obtain the steady attitude matrix, the problem can be transformed into a Wahba problem by constructing vector observations. In 1965, Wahba first proposed the attitude determination method of vector observation and pointed out that the optimal attitude matrix minimizes the loss function. There are two ways to solve the Wahba problem. One is a deterministic algorithm, such as SVD, Fast Linear Attitude Estimator (FLAE) and Quaternion Estimator (QUEST). The other is a random algorithm, such as recursive QUEST (Recursive QUEST, REQUEST), optimal REQUEST (Optimal-REQUEST, OPREQ) and matrix Kalman filter (Matrix Kalman filter, MKF). Although these methods can effectively solve the initial alignment problem of inertial navigation in conventional scenarios, they still cannot solve the contradiction between initial alignment accuracy and alignment time. Coarse alignment sacrifices accuracy for short time, and fine alignment sacrifices Time trades off for high accuracy. Therefore, in highly complex and highly dynamic environments, how to effectively weigh alignment accuracy and alignment time has become an urgent problem that needs to be solved.

Contents of the invention

In order to overcome the shortcomings of the existing technology, the present invention proposes a relay-type rapid aerial alignment method, which combines the rapidity of the optimization algorithm and the high precision of the filtering algorithm to complement each other's advantages and effectively solve the conflicting problem of alignment accuracy and alignment time. , comprehensively improve the air aiming performance of guided artillery shells.

The technical solution adopted by the present invention is: a relay-type rapid aerial alignment method. First, the initial attitude angle is used as the optimization object to construct an optimization model in the optimization stage, and then the filtering stage in the filtering stage is constructed based on the optimal initial attitude angle obtained in the optimization stage. model; then based on the adaptive multi-constraint mode, the internal relay method in the optimization stage and the external relay method in the transition from the optimization stage to the filtering stage are designed to determine the initial attitude and achieve alignment.

Further, in the optimization stage, the optimization model is used as the fitness function, and an intelligent optimization algorithm and a sliding window are used for optimization.

Further, the optimization model is:

In the formula, (θ ₀ ,γ ₀ ,ψ ₀ ) represents the initial attitude angle; ||·|| represents the 2-norm, attitude matrix

, and/> is the observation vector at time t _k .

Further, the internal relay methods in the design optimization stage include:

The optimization model based on the sliding window determines J _k , determines δA _k through δA _k =A _max J _k rand, and determines the upper bound UB _k+1 and the lower bound LB _k of the initial population of the intelligent optimization algorithm through A _k and δA _k . ₊₁ ; where A _max represents the maximum value of the initial attitude, rand represents a uniformly distributed random number between [0,1], A _k represents the optimal initial posture obtained within the sliding window at time k, and δA _k represents the controllable range;

If the upper bound UB _k+1 >A _max , then UB _k+1 =A _max ; if the indeterminate bound LB _k+1 <A _min , then LB _k+1 =A _min , and A _min represents the minimum initial attitude value.

Furthermore, the external relay methods for transitioning from the optimization stage to the filtering stage specifically include:

Determine the relay function from the optimization stage to the filtering stage based on the loss proportion;

If the relay function is greater than the relay threshold, the optimal initial attitude angle obtained in the optimization stage will be Convert to quaternion/> form, in terms of quaternions/> Determine the initial state matrix X ₀ of the filter model to complete the external force, otherwise continue to seek optimization through the optimization stage.

Further, the filtering model for constructing the filtering stage includes:

According to the observation vector at time t _k and/> Calculate the matrix after normalization/>

In the formula,

According to matrix The eigenvector corresponding to the maximum eigenvalue can be used to obtain the initial posture matrix/> The state equation of the K _k matrix is obtained: K _k =K _k-1 ;

Let the state estimation matrix X _k =K _k and the observation matrix be The artillery shell air alignment filter model is established as:

In the formula, matrix F = I ₄ , H = I ₄ , where I ₄ is the unit matrix, W _k and V _k are system noise and measurement noise respectively, and satisfy:

In the formula, vec( ) is the vectorization operator, q _k is the mean value of system noise, r _k is the mean value of measurement noise, Q _k is the mean square error of system noise, and R _k is the mean square error of system measurement noise.

Further, the relay function is:

In the formula, p _k is the loss proportion.

Further, the relay threshold is 10.

Compared with the prior art, the beneficial effects of the present invention are:

(1) This method is mainly divided into optimization stage and filtering stage. First, the initial attitude angle is used as the optimization object to build an optimization model, and then the K matrix is used as the state variable to build a filtering model; then the internal relay method of the optimization stage and the transition to the optimization stage are designed. The external relay mode of the filtering stage uses the adaptive multi-constraint mode to take advantage of the rapidity of the optimization algorithm to speed up the alignment process; the filtering stage is used as the main body to take advantage of the high-precision features of the filtering algorithm to improve alignment accuracy;

(2) The constraints in the internal relay stage of this method are based on the loss function value in the current sliding window, and the optimization algorithm in the next sliding window is designed to generate the upper and lower bounds of the initial population, thereby limiting the search range, so that the optimization algorithm can quickly and accurately search for the optimal The optimal initial attitude angle; the constraint in the external relay stage is to design the relay function based on the loss ratio to determine the timing of transition from the optimization stage to the filtering stage, and convert the optimal initial attitude angle obtained in the optimization stage into K matrix form, and As the initial value of the filtering stage state, to improve the speed and high accuracy of the filtering algorithm.

Description of the drawings

Figure 1 is a flow chart of the method of the present invention.

Figure 2 is a schematic diagram of the optimization stage.

Figure 3 is a frame diagram of artillery relay type aerial alignment.

Detailed ways

Next, the implementation of the present invention will be described in detail with reference to the accompanying drawings.

Aerial alignment is the basis for the artillery shell strapdown inertial navigation system (SINS) to achieve accurate navigation. The micro-inertial navigation aerial alignment of guided artillery shells faces "high" complexity such as satellite interference and random wind disturbance, high speed, high rotation, high overload, etc. "High" dynamics and other challenges, for this reason, this embodiment provides a relay-type fast aerial alignment method. Combined with Figure 1, this method is mainly divided into an optimization stage and a filtering stage. First, the initial attitude angle is used as the optimization object to build an optimization model. , and then use the K matrix as the state variable to build a filter model; then design the internal relay method of the optimization stage and the external relay method of the transition from the optimization stage to the filter stage, and use the adaptive multi-constraint mode to take advantage of the rapidity of the optimization algorithm and speed up the alignment process; The filtering stage is used as the main body to give full play to the high-precision characteristics of the filtering algorithm and improve the alignment accuracy. The constraints in the inner relay stage are mainly based on the loss function value in the current sliding window, and the optimization algorithm in the next sliding window is designed to generate the upper and lower bounds of the initial population. Thereby limiting the search range, the optimization algorithm can quickly and accurately search for the optimal initial attitude angle. The constraint in the external relay stage is to design the relay function based on the loss ratio to determine the timing of transition from the optimization stage to the filtering stage, and use the results obtained in the optimization stage The optimal initial attitude angle is converted into K matrix form, which is used as the initial value of the filtering stage state to improve the speed and high accuracy of the filtering algorithm. The method will be described in detail next.

The key issue in the air alignment of artillery shells is to determine the attitude matrix from the projectile coordinate system to the navigation coordinate system This paper mainly studies the initial alignment problem of GNSS-assisted SINS during the flight of artillery shells. The alignment process starts from time 0.

According to the chain rule, the attitude matrix Can be broken down into:

In the formula, the navigation coordinate system at time t is n(t), and the missile coordinate system is b(t). The navigation coordinate system at time 0 is n(0), and the missile coordinate system is b(0).

According to the velocity differential equation of SINS:

In the formula, R _e is the average radius of the earth, ω _ie is the earth's rotation angular rate, [L λ h] ^T is the position, representing latitude, longitude and altitude respectively,/> are speeds, representing east, north and celestial speeds respectively. f ^b is the three-axis specific force measured by the accelerometer, and g ⁿ is the local gravity acceleration.

Since the flight time of the cannonball is short and the impact point is close, it can be considered that the navigation coordinate system n does not change, then:

By combining equation (2) and equation (3) and integrating both sides of the equation at the same time, we can get:

In the formula, It can be obtained by the rotation vector method.

Simplified formula (4) can be obtained:

In the formula,

and/> The specific recursive solution is as follows:

The solution to equation (5) is the Wahba problem. Converting it into an optimization problem, the fitness function can be constructed as:

In the formula, (θ ₀ , γ ₀ , ψ ₀ ) represents the initial attitude angle; ||·|| represents the 2-norm.

Equation (7) is the air alignment optimization model. Theoretically, J(θ ₀ , γ ₀ , ψ ₀ )=0 in Equation (7). However, since this equation is a transcendental equation, it cannot be solved directly and the optimal solution needs to be found. The initial posture satisfies equation (7). Therefore, equation (7) can be used as the fitness function, with the initial attitude angle as the optimization object, and an intelligent optimization algorithm can be used to achieve aerial alignment.

According to the observation vector at time t _k and/> Calculate after normalization/> matrix:

In the formula,

according to The eigenvector corresponding to the maximum eigenvalue of the matrix can be used to obtain the initial posture matrix/> Theoretically speaking,/> should be constant, therefore, the state equation of the _K matrix is:

K _k =K _k-1 (9)

According to equations (8) and (9), let the state estimation matrix X _k =K _k and the observation matrix be The artillery shell air alignment filter model can be established:

In the formula, F=I ₄ , H=I ₄ , and I ₄ is the unit matrix. W _k and V _k are system noise and measurement noise respectively, and satisfy:

In the formula, vec() is the vectorization operator.

MKF can be used to solve equation (10) to obtain the optimal _K matrix, thereby extracting the initial attitude angle and realizing the alignment process.

Relay-type air alignment is mainly divided into optimization stage and filtering stage. "Relay" is mainly divided into internal relay method in the optimization stage and external relay method in the transition from the optimization stage to the filtering stage.

In the optimization phase, the sliding window is used for optimization. On the one hand, it reduces the number of optimization algorithm searches and speeds up the optimization phase. On the other hand, the sliding window can reduce the impact of noise on the optimization results. For this purpose, equation (7) is changed to:

In the formula, N represents the length of the sliding window.

Combined with Figure 2, the internal relay method mainly occurs between two sliding windows. Taking k time as an example, the intelligent optimization algorithm can be used to obtain the optimal initial posture A _k within the sliding window at k time, and transfer A _k to k + 1 time, providing a range reference for the intelligent optimization algorithm to generate the initial population within the k+1 time sliding window, that is

In the formula, UB _k+1 represents the upper bound of the initial population of the intelligent optimization algorithm within the sliding window at time k+1, LB _k+1 represents the lower bound of the initial population of the intelligent optimization algorithm within the sliding window at time k+1, A _k represents the optimal initial attitude obtained within the sliding window at time k, and δA _k represents the controllable range.

As can be seen from Figure 2, the optimal initial posture obtained within each sliding window will gradually be passed on, and the accuracy of the initial posture directly determines the size of the loss function (12). When the value obtained by the loss function in the current sliding window is large, it means that the initial attitude error obtained is large. When generating the initial population in the next sliding window, it is necessary to expand the range of the upper and lower bounds, that is, increase δA _k ; when the loss function When the value obtained in the current sliding window is small, it means that the initial attitude error obtained is small. When the initial population is generated in the next sliding window, the upper and lower bounds can be narrowed, that is, δA _k can be reduced. Therefore, the linear relationship between δA _k and J _k can be constructed, that is

δA _k =A _max J _k rand (14)

In the formula, A _max represents the maximum value of the initial attitude, that is, the maximum value of the search; rand represents a random number obeying a uniform distribution between [0,1].

The specific process of the internal relay method is as follows:

In the optimization stage, the intelligent optimization algorithm is used to quickly lock in the vicinity of the true initial posture. In the filtering stage, the MKF algorithm is used to slowly estimate the true initial posture. The moment of transition from the optimization stage to the filtering stage is crucial. Taking inspiration from information entropy, define the loss proportion as:

According to equation (15), it can be seen that as the sliding window moves, p _k gradually decreases in the form of an inverse proportional function, which means the proportion of the loss calculated by the current loss function in the historical loss. When its proportion is reduced to a certain level This will then lead to the filtering stage. For convenience of expression, take the logarithm of both sides of equation (15) to obtain the relay function:

In the formula, Hp _k is the relay function, which mainly determines the moment of transition from the optimization stage to the filtering stage. This article sets the relay to start when Hp _k ≥ 10, and at this time p _k ≤ 10 ^-10 .

In the optimization stage, a rough optimal initial attitude angle can be obtained In the filtering stage, the _K matrix is used as the quantity to be estimated. For this purpose, it is necessary to Convert to _K matrix. There is another form of equation (12), namely

In the formula, q represents the attitude quaternion corresponding to the initial attitude angle, q ^T q=1.

According to equation (17), it can be seen that theoretically q ^T K _k q=1, and a specific solution K _k =qq ^T can be obtained. Therefore, the results obtained during the optimization phase are Convert to quaternion/> Available,

Take equation (18) as the initial state matrix of MKF in the filtering stage, that is Thus completing the external relay process. The specific process of external relay method is as follows:

To sum up, the artillery relay aerial alignment framework is shown in Figure 3. The relay aerial alignment is mainly divided into the optimization stage and the filtering stage. The "relay" is mainly divided into the internal relay mode of the optimization stage and the transition from the optimization stage to the filtering stage. external relay method.

In the optimization stage, intelligent optimization algorithms such as particle swarm optimization algorithm and genetic algorithm can be used to optimize the initial posture.

The above-described embodiments only express the implementation of the present application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be noted that, for those of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present application, and these all fall within the protection scope of the present application. Therefore, the protection scope of this patent application should be determined by the appended claims.

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.