阅读说明：本技术 一种基于方位角及其变化率的目标运动分析方法 (Target motion analysis method based on azimuth angle and change rate thereof ) 是由 齐滨 邹男 付进 董彦璐 王晋晋 郝宇 王路 于 2020-12-28 设计创作，主要内容包括：本发明设计了一种基于方位角及其变化率的目标运动分析方法：首先设定坐标系,根据几何关系求得方位角及其变化率与目标位置速度之间的表达式,构建关于方位角及其变化率的误差方程,并转换成伪线性形式,构建量测增广矩阵和增广解,然后将含有噪声信息的量测方位角及方位角变化率代入构建的量测增广矩阵中,得到一个由噪声引起的矩阵,将该矩阵的转置与该矩阵的乘积的均值设为约束矩阵,再对误差方程进行最小二乘极小化处理,利用拉格朗日乘子法求在约束条件下的误差方程的最小二乘解,最后利用几何关系求出目标各时刻的方位信息并平滑处理,得到定位结果。(The invention designs a target motion analysis method based on an azimuth angle and a change rate thereof, which comprises the following steps: firstly, setting a coordinate system, obtaining an expression between an azimuth angle and a change rate thereof and a target position speed according to a geometric relation, constructing an error equation about the azimuth angle and the change rate thereof, converting the error equation into a pseudo-linear form, constructing a measurement augmentation matrix and an augmentation solution, then substituting the measurement azimuth angle containing noise information and the change rate of the azimuth angle into the constructed measurement augmentation matrix to obtain a matrix caused by noise, setting the average value of the product of the transposition of the matrix and the matrix as a constraint matrix, then carrying out least square minimization processing on the error equation, obtaining the least square solution of the error equation under the constraint condition by using a Lagrange multiplier method, finally obtaining azimuth information of each moment of the target by using the geometric relation and carrying out smoothing processing to obtain a positioning result.)

1. A target motion analysis method based on azimuth angles and change rates thereof is characterized in that:

the method specifically comprises the following steps:

the method comprises the following steps: setting a coordinate system, solving an expression between the azimuth angle and the change rate thereof as well as the target position speed according to the geometric relationship, constructing an error equation about the azimuth angle and the change rate thereof, and converting the error equation into a pseudo-linear form;

step two: constructing a measurement augmentation matrix and an augmentation solution, and changing the form of an error equation;

step three: substituting the measurement azimuth angle containing the noise information and the azimuth angle change rate into the measurement augmentation matrix constructed in the second step to obtain a matrix caused by the noise, and setting the mean value of the product of the transpose of the matrix and the matrix as a constraint matrix;

step four: performing least square minimization on the error equation in the second step, solving a least square solution of the error equation related to the azimuth angle and the change rate thereof, which is constructed in the second step under the constraint condition, by using a Lagrange multiplier method, wherein the result after equation simplification is substantially the process of solving the characteristic vector under the characteristic value, and the obtained least square solution is an augmentation solution in the second step and contains the x coordinate of the target initial moment and the speed of the target;

step five: and substituting the target information obtained in the fourth step into a motion equation to obtain the position information of the target in the x direction at each moment, obtaining the position information of the target in the y direction at each moment by using a geometric relation, and smoothing to obtain a final positioning result.

2. The method of claim 1, further comprising: in the first step:

setting a rectangular coordinate system, and expressing the target position as [ x ] at the moment i_T(i),y_T(i)]The velocity is expressed asObserver position is denoted as [ x ]_O(i),y_O(i)]The velocity is expressed asThe azimuth angle is the angle between the line connecting the target and the observer and the y-axis, denoted by beta,as a result of the rate of change of the azimuth angle,and expressing the change rate of the azimuth angle at the moment i and the expressions between the change rate of the azimuth angle and the positions and the speeds of the target and the observer through a geometrical relation:

wherein the content of the first and second substances,the speed difference between the target at the moment i and the x direction of an observer is obtained;

Δ x is the distance difference between the target and the observer at time i in the x direction;

the speed difference between the target and the observer at the moment i in the y direction;

Δ y is the distance difference between the target and the observer at time i in the y direction;

r is the distance between the target and the observer at time i;

because the target moves at a constant speed, the target can obtainWhere T is the unit observation time interval, the error equation is derived from the above equation, the error epsilon at time i_iComprises the following steps:

now setting unknown parametersMeasurement vector g

And a measurement matrix A, which is used to measure the measurement matrix A,

the error epsilon is expressed as the pseudolinearity form epsilon as A mu-g, i.e.

3. The method of claim 2, further comprising: in the second step:

constructing a measurement augmentation matrix A_new＝[A,-g]And extended solution θ ═ h [ mu ]^T,1]^TWhere h is a constant, the error is ε ═ A_newθ/h，

Wherein the content of the first and second substances,

4. the method of claim 3, further comprising: in step three:

the variation range of the azimuth angle beta is 0-2 pi,for the real azimuth information at time i, e_βFor azimuthal measurement error, e_β,iMeasuring error of azimuth angle at the moment i;

rate of change of azimuthThe value of (a) is of the order of mrad/s,the true azimuthal rate of change at time i,for the measurement error of the rate of change of the azimuth angle,the measurement error is the azimuth angle change rate at the moment i;

therefore, in the simulation, the standard deviation of the azimuth angle measurement noise is set to be pi/100, the standard deviation of the azimuth angle change rate measurement noise is set to be 0.1mrad/s, and cos (2 e)_β,i)≈1，sin(2e_β,i)≈2e_β,iWill beAndsubstituted into A_newTo obtain

A_newIn order to measure the augmented matrix, the measurement matrix is,to bring the true azimuth angle and its rate of change into A_newThe results obtained;

constraint matrixE is the desired symbol.

5. The method of claim 4, further comprising: in step four:

solving in quadratic constraint theta by using Lagrange multiplier method^TA least squares solution of an error equation with W θ being a constant, the quadratic constraint θ^TW theta is an arbitrary value, the constant is adjusted by h in theta, and a constraint condition theta is set^TW theta is 1, and a function is obtainedWherein lambda is Lagrange multiplier, and partial derivative of xi to theta is taken to obtainThen solve forThe minimum eigenvector under the eigenvalue lambda is the augmentation solution theta in the step two, and the unknown parameter mu is according to the formula

That is, the x-coordinate of the initial time of the target and the speed of the target can be obtained.

6. The method of claim 5, further comprising: in the fifth step:

using formulasObtaining the x coordinate of the target at the moment i, combining the azimuth angle information and according to a formulaAnd obtaining the y coordinate of the target at the moment, and smoothing the estimated target position to obtain the final positioning result.

Technical Field

The invention relates to the field of passive positioning of underwater targets, in particular to a target motion analysis method based on an azimuth angle and a change rate thereof.

Background

The underwater target positioning is an important direction of underwater acoustic engineering research, the target motion analysis technology is to utilize an algorithm to calculate a motion model of an unknown target to estimate position information of the target, and the passive target motion analysis technology has the advantages of long action distance and strong concealment, improves the survival capability and the working capability of the system in a complex and changeable underwater environment, and is widely concerned by people. The underwater passive target motion analysis technology of the single array is more practical due to the advantages of simplicity, convenience, flexibility and low cost. The traditional target motion analysis mode is mainly a pure azimuth target motion analysis method, and requires that the platform has at least one effective maneuver to meet observability requirements.

Disclosure of Invention

The method utilizes the azimuth angle and the change rate information thereof to carry out least square minimization processing on a pseudo linear equation set with secondary constraint on the estimated parameters so as to realize the passive positioning of the underwater target, and is suitable for the condition that the maneuvering target of the platform is uniform.

A target motion analysis method based on an azimuth angle and a change rate thereof specifically comprises the following steps:

the method comprises the following steps: setting a coordinate system, solving an expression between the azimuth angle and the change rate thereof as well as the target position speed according to the geometric relationship, constructing an error equation about the azimuth angle and the change rate thereof, and converting the error equation into a pseudo-linear form;

step two: constructing a measurement augmentation matrix and an augmentation solution, and changing the form of an error equation;

step three: substituting the measurement azimuth angle containing the noise information and the azimuth angle change rate into the measurement augmentation matrix constructed in the second step to obtain a matrix caused by the noise, and setting the mean value of the product of the transpose of the matrix and the matrix as a constraint matrix;

step four: performing least square minimization on the error equation in the second step, solving a least square solution of the error equation related to the azimuth angle and the change rate thereof, which is constructed in the second step under the constraint condition, by using a Lagrange multiplier method, wherein the result after equation simplification is substantially the process of solving the characteristic vector under the characteristic value, and the obtained least square solution is an augmentation solution in the second step and contains the x coordinate of the target initial moment and the speed of the target;

step five: and substituting the target information obtained in the fourth step into a motion equation to obtain the position information of the target in the x direction at each moment, obtaining the position information of the target in the y direction at each moment by using a geometric relation, and smoothing to obtain a final positioning result.

Further: in the first step:

setting a rectangular coordinate system, and expressing the target position as [ x ] at the moment i_T(i),y_T(i)]The velocity is expressed asObserver position is denoted as [ x ]_O(i),y_O(i)]The velocity is expressed asThe azimuth angle is the angle between the line connecting the target and the observer and the y-axis, denoted by beta,as a result of the rate of change of the azimuth angle,and expressing the change rate of the azimuth angle at the moment i and the expressions between the change rate of the azimuth angle and the positions and the speeds of the target and the observer through a geometrical relation:

wherein the content of the first and second substances,the speed difference between the target at the moment i and the x direction of an observer is obtained;

Δ x is the distance difference between the target and the observer at time i in the x direction;

the speed difference between the target and the observer at the moment i in the y direction;

Δ y is the distance difference between the target and the observer at time i in the y direction;

r is the distance between the target and the observer at time i;

because the target moves at a constant speed, the target can obtainWhere T is the unit observation time interval, the error equation is derived from the above equation, the error epsilon at time i_iComprises the following steps:

now setting unknown parametersMeasurement vector g

And a measurement matrix A, which is used to measure the measurement matrix A,

the error epsilon is expressed as the pseudolinearity form epsilon as A mu-g, i.e.

Further: in the second step:

constructing a measurement augmentation matrix A_new＝[A,-g]And extended solution θ ═ h [ mu ]^T,1]^TWhere h is a constant, the error is ε ═ A_newθ/h，

Wherein the content of the first and second substances,

further: in step three:

the variation range of the azimuth angle beta is 0-2 pi,for the real azimuth information at time i, e_βFor azimuthal measurement error, e_β,iMeasuring error of azimuth angle at the moment i;

rate of change of azimuthThe value of (a) is of the order of mrad/s,the true azimuthal rate of change at time i,for the measurement error of the rate of change of the azimuth angle,is when i isMeasuring error of azimuth angle change rate;

therefore, in the simulation, the standard deviation of the azimuth angle measurement noise is set to be pi/180, the standard deviation of the azimuth angle change rate measurement noise is set to be 0.1mrad/s, and cos (2 e)_β,i)≈1，sin(2e_β,i)≈2e_β,iWill beAndsubstituted into A_newTo obtain

A_newIn order to measure the augmented matrix, the measurement matrix is,to bring the true azimuth angle and its rate of change into A_newThe results obtained;

constraint matrixIs the desired symbol.

Further: in step four:

solving in quadratic constraint theta by using Lagrange multiplier method^TA least squares solution of an error equation with W θ being a constant, the quadratic constraint θ^TW theta is an arbitrary value, the constant is adjusted by h in theta, and a constraint condition theta is set^TW theta is 1, and a function is obtainedWherein lambda is Lagrange multiplier, and partial derivative of xi to theta is taken to obtainThen solve forThe minimum eigenvector under the eigenvalue lambda is the augmentation solution theta in the step two, and the unknown parameter mu is according to the formula

That is, the x-coordinate of the initial time of the target and the speed of the target can be obtained.

Further: in the fifth step:

using formulasObtaining the x coordinate of the target at the moment i, combining the azimuth angle information and according to a formulaAnd obtaining the y coordinate of the target at the moment, and smoothing the estimated target position to obtain the final positioning result.

The invention has the beneficial effects

1. The invention carries out least square minimization on a pseudo linear equation set with secondary constraint on estimation parameters, and finally converts the solution of the estimator into the problem of solving the eigenvector under the characteristic value by using a Lagrange multiplier method.

2. The method does not need initial pre-estimated parameters, has unbiased estimated values, has higher precision and faster convergence speed compared with the traditional pure-azimuth underwater target motion analysis method, and rapidly reduces the estimated error of the target position and speed until the estimated error is stable along with the increase of the iteration times.

Drawings

FIG. 1 is a flow chart of an underwater target motion analysis method based on azimuth and its rate of change in accordance with the present invention;

FIG. 2 is a geometric diagram of the subject and observer of the present invention;

FIG. 3 is a diagram of the trajectory of the movement of the target and the observer in the simulation of the present invention;

FIG. 4 is a comparison of the true trajectory of the algorithm target and the estimated trajectory in the simulation of the present invention;

FIG. 5 is a graph of target distance estimation error in the simulation of the present invention;

FIG. 6 is a graph of target velocity estimation error in the simulation of the present invention.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments; all other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

Setting the initial position of a uniform-speed moving target as (3000m,0m), the moving speed of the target as 5m/s, the included angle between the moving direction of the target and the due north direction as pi/6, the initial position of an observer as (0m,0m), the moving speed of the observer as 10m/s, maneuvering at 200s, 400s, 600s and 800s respectively, the angle of each maneuvering being pi/2, the heading change speed as (pi/180) rad/s, and a situation diagram as shown in fig. 3, wherein the main steps of the algorithm are as shown in fig. 1, and specifically, the following steps are performed:

a target motion analysis method based on an azimuth angle and a change rate thereof specifically comprises the following steps:

the method comprises the following steps: setting a coordinate system, solving an expression between the azimuth angle and the change rate thereof as well as the target position speed according to the geometric relationship, constructing an error equation about the azimuth angle and the change rate thereof, and converting the error equation into a pseudo-linear form;

step two: constructing a measurement augmentation matrix and an augmentation solution, and changing the form of an error equation;

step three: substituting the measurement azimuth angle containing the noise information and the azimuth angle change rate into the measurement augmentation matrix constructed in the second step to obtain a matrix caused by the noise, and setting the mean value of the product of the transpose of the matrix and the matrix as a constraint matrix;

step four: performing least square minimization on the error equation in the second step, solving a least square solution of the error equation related to the azimuth angle and the change rate thereof, which is constructed in the second step under the constraint condition, by using a Lagrange multiplier method, wherein the result after equation simplification is substantially the process of solving the characteristic vector under the characteristic value, and the obtained least square solution is an augmentation solution in the second step and contains the x coordinate of the target initial moment and the speed of the target;

step five: and substituting the target information obtained in the fourth step into a motion equation to obtain the position information of the target in the x direction at each moment, obtaining the position information of the target in the y direction at each moment by using a geometric relation, and smoothing to obtain a final positioning result.

In the first step:

setting a rectangular coordinate system, and expressing the target position as [ x ] at the moment i_T(i),y_T(i)]The velocity is expressed asObserver position is denoted as [ x ]_O(i),y_O(i)]The velocity is expressed asThe azimuth angle is the angle between the line connecting the target and the observer and the y-axis, denoted by beta,as a result of the rate of change of the azimuth angle,and expressing the change rate of the azimuth angle at the moment i and the expressions between the change rate of the azimuth angle and the positions and the speeds of the target and the observer through a geometrical relation:

wherein the content of the first and second substances,is composed ofThe speed difference between the time target and the observer in the x direction;

Δ x is the distance difference between the target and the observer at time i in the x direction;

the speed difference between the target and the observer at the moment i in the y direction;

Δ y is the distance difference between the target and the observer at time i in the y direction;

r is the distance between the target and the observer at time i;

because the target moves at a constant speed, the target can obtainWhere T is the unit observation time interval, the error equation is derived from the above equation, the error epsilon at time i_iComprises the following steps:

now setting unknown parametersMeasurement vector g

And a measurement matrix A, which is used to measure the measurement matrix A,

the error epsilon is expressed as the pseudolinearity form epsilon as A mu-g, i.e.

In the second step:

constructing a measurement augmentation matrix A_new＝[A,-g]And extended solution θ ═ h [ mu ]^T,1]^TWhere h is a constant, the error is ε ═ A_newθ/h，

Wherein the content of the first and second substances,

in step three:

the variation range of the azimuth angle beta is 0-2 pi,for the real azimuth information at time i, e_βFor azimuthal measurement error, e_β,iMeasuring error of azimuth angle at the moment i;

rate of change of azimuthThe value of (a) is of the order of mrad/s,is when i isThe rate of change of the true azimuth angle is,for the measurement error of the rate of change of the azimuth angle,the measurement error is the azimuth angle change rate at the moment i;

therefore, in the simulation, the standard deviation of the azimuth angle measurement noise is set to be pi/180, the standard deviation of the azimuth angle change rate measurement noise is set to be 0.1mrad/s, and cos (2 e)_β,i)≈1，sin(2e_β,i)≈2e_β,iWill beAndsubstituted into A_newTo obtain

A_newIn order to measure the augmented matrix, the measurement matrix is,to bring the true azimuth angle and its rate of change into A_newThe results obtained;

constraint matrixIs the desired symbol.

In step four:

solving in quadratic constraint theta by using Lagrange multiplier method^TA least squares solution of an error equation with W θ being a constant, the quadratic constraint θ^TW theta is an arbitrary value, the constant is adjusted by h in theta, and a constraint condition theta is set^TW theta is 1, and a function is obtainedWherein lambda is Lagrange multiplier, and partial derivative of xi to theta is taken to obtainThen solve forThe minimum eigenvector under the eigenvalue lambda is the augmentation solution theta in the step two, and the unknown parameter mu is according to the formula

That is, the x-coordinate of the initial time of the target and the speed of the target can be obtained.

In the fifth step:

using formulasObtaining the x coordinate of the target at the moment i, combining the azimuth angle information and according to a formulaAnd obtaining the y coordinate of the target at the moment, and smoothing the estimated target position to obtain the final positioning result.

As shown in fig. 4, compared with the real target trajectory, it can be seen that the solution result of the method substantially matches the actual trajectory. As can be seen from the error graphs of fig. 5 and 6, as the number of iterations increases, the estimation error of the target position and the speed decreases rapidly until the target position and the speed tend to be stable, the distance error tends to be about 100 meters, and the speed error tends to be about 0.2 meter/second, which indicates that the method can obtain a good positioning result.

The above detailed description is provided for a target motion analysis method based on azimuth and its change rate, and the principle and implementation of the present invention are explained, and the above description of the embodiment is only used to help understanding the method and its core idea of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, there may be variations in the specific embodiments and the application scope, and in summary, the content of the present specification should not be construed as a limitation to the present invention.