阅读说明：本技术 惯性量匹配对准的角形变测量误差评估方法 (Angular deformation measurement error evaluation method for inertial quantity matching alignment ) 是由 秦石乔 张羽彤 马相路 吴伟 郑佳兴 王省书 谭文锋 于 2019-10-25 设计创作，主要内容包括：本发明公开了一种惯性量匹配对准的角形变测量误差评估方法,建立了角速度匹配形变测量误差大小的相关函数表达式,其误差大小不仅与船体角速度的自相关函数有关,而且与船体角速度与动态形变角速度分量误差的互相关函数有关。基于Kalman滤波误差协方差矩阵理论,提出了一种用协方差矩阵元素描述动态形变角速度分量误差大小的方法,引进了调整优化系数,得到了完整的形变角误差估算公式,使误差估算结果能更好地描述真实误差的变化。通过实测的船体形变数据进行验证,结果表明估算公式具有较好的误差估算效果。(The invention discloses an angular deformation measurement error evaluation method for inertia quantity matching alignment, which establishes a correlation function expression of the angular velocity matching deformation measurement error, wherein the error is not only related to an autocorrelation function of a hull angular velocity, but also related to a cross-correlation function of the hull angular velocity and a dynamic deformation angular velocity component error.)

1, kinds of methods for estimating angular deformation measurement errors in inertial mass matching alignment, comprising the steps of:

1) setting sequence data length k and adjusting an optimization coefficient F;

2) according to the IMU measured value, times of kalman matched filtering is carried out to obtain the cross elements of the covariance matrix

3) By usingCalculating the error of each axial component of the measurement of the inertia quantity matched with the dynamic deformation angular velocity

4) Using errors of respective axial components

2. The method of estimating angular deformation measurement error in inertial mass matching alignment of claim 1, wherein each axial component error is estimated by a single error estimatorThe calculation formula of (2) is as follows:

3. The angular deformation measurement error evaluation method of the inertia mass matching alignment according to claim 2, wherein in the X direction, F ═ 1.4; in the Y direction, F is 0.8; in the Z direction, F ═ 2.

4. The angular deformation measurement error evaluation method for inertial mass matching alignment according to claim 1, wherein, in step 4),

wherein, ω is_x(i)、ω_y(i)、ω_z(i) Angular velocity vector data of the IMU mounting position with respect to the inertial space is acquired for the sub-IMUs.

Technical Field

The invention relates to the field of inertial navigation, in particular to an angular deformation measurement error evaluation method for matching and aligning inertial quantities.

Background

The modern warship is equipped with various sensors and weapon systems, such as radars, missiles, optical sights and the like, in order to ensure that different systems on the ship can work with each other, a system reference coordinate system is required to be established, however, the ship body can deform due to movement, load change, temperature change and the like, so that the established system reference coordinate system is out of alignment, the deformation of the ship body is measured by using an inertia matching measurement method, the system has the advantages of convenience in use, capability of simultaneously measuring angular deformation and position deformation, high measurement precision and the like, the deformation result can be compensated through the accurate measurement of the deformation of the ship body, so that the coordinate system on the ship body is not influenced by the deformation.

Disclosure of Invention

The invention aims to solve the technical problem that methods for estimating the angular deformation measurement error of inertial quantity matching alignment are provided aiming at the defects of the prior art, so that the error estimation result can better describe the change of a real error.

In order to solve the technical problem, the invention adopts the technical scheme that the angular deformation measurement error evaluation method for matching and aligning kinds of inertia quantity comprises the following steps:

1) setting sequence data length k and adjusting an optimization coefficient F;

2) according to the IMU measured value, times of kalman matched filtering is carried out to obtain the cross elements of the covariance matrix

3) By using

Calculating the error of each axial component of the measurement of the inertia quantity matched with the dynamic deformation angular velocity

4) Using errors of respective axial components

Calculating the error of each axial component of the inertial matching alignment angle deformation measurement

Error of each axial componentThe calculation formula of (2) is as follows:

wherein F is an adjusting optimization coefficient.

In the X direction, F is 1.4; in the Y direction, F is 0.8; in the Z direction, F ═ 2.

In the step 4), the step of mixing the raw materials,the calculation formula of (2) is as follows:

wherein, ω is_x(i)、ω_y(i)、ω_z(i) Angular velocity vector data of the IMU mounting position with respect to the inertial space is acquired for the sub-IMUs.

Compared with the prior art, the method has the advantages that a correlation function expression of angular velocity matching deformation measurement error magnitude is established, methods for describing dynamic deformation angular velocity component error magnitude by using covariance matrix elements are provided based on Kalman filtering error covariance matrix theory, adjustment optimization coefficients are introduced, a complete deformation angle error estimation formula is obtained, and the error estimation result can better describe the change of a real error.

Drawings

Figure 1 is a schematic view of the installation of two IMUs at different locations on a ship.

Fig. 2 is a processing flow chart corresponding to the implementation steps of the present invention.

FIG. 3 shows the relationship between the error estimation and the value of the tuning optimization coefficient F in the X-direction F, which is 0-2.

FIG. 4 shows the relationship between the error estimation and the value of the tuning optimization coefficient F between Y-direction F and 0 ~ 2.

FIG. 5 shows the relationship between the error estimation and the value of the tuning optimization coefficient F between the Z direction F and 0-2.

Fig. 6 shows the relationship between the error estimate and the true error when the X direction F is 1.4.

Fig. 7 shows the relationship between the error estimate and the true error when the Y direction F is 0.8.

Fig. 8 shows the relationship between the error estimate and the true error when the Z direction F is 2.

Detailed Description

The main ideas of the invention are as follows: in the deformation measurement method based on angular velocity matching alignment, due to the coupling effect of the angular motion and the angular deformation of the ship body, the optimal estimation filter based on least square generates fixed deviation when estimating deformation. And (4) deriving an error estimation formula of the static deformation estimation error by using a correlation function theory. Cross element using covariance matrix

To describe the dynamic deformation angular velocity error

And an optimization coefficient F is introduced to adjust the estimation error to be close to the real error variation range.

The deformation Measurement of the matching alignment of the Inertia quantity is composed of two Inertia Measurement Units (IMU) installed at different positions of the ship, as shown in fig. 1. Each IMU mainly comprises three accelerometers and three gyroscopes, and angular velocity vectors of the IMU installation position relative to an inertial space are measured

The two IMUs are denoted by IMUm and IMUs, respectively, and the corresponding angular velocity vector measurements are used, respectively

And

the upper subscripts s, m, i denote the child, master IMU and inertial frame, respectively. The most commonly used deformation measurement inertia is the angular velocity vector, and the corresponding deformation measurement equation is:

(1) in the formula (I), the compound is shown in the specification,in order to be the angular velocity vector difference,

is a direct current vector of angular deformation, also called static deformation,

is an alternating current vector, also called dynamic deformation,

is an antisymmetric matrix.

For the actually sampled discrete data sequence vector, the formula (1) can be rewritten as a matrix equation:

(2) the coefficient matrix in the formula is:

k is the sampling ordinal number. (2) The error solved by the least square method is respectively

And

then there are:

the least squares estimate of (d) is:

when the sampled data k is sufficiently large, k → ∞, according to sinkian law of large numbers,

will converge to, on probability:

(6) in the formula, R represents a correlation function,

is omega_yAn autocorrelation function with a self delay time of 0,

is omega_zAnd

the matrix to the right of the equal sign of equation (6) takes the inverse as the denominator, with the diagonal elements being the autocorrelation function of the ship's roll angular velocity and the off-diagonal elements being the cross correlation function of the ship's roll angular velocity.

According to the kalman filtering theory, the covariance matrix P describes the variance of the state quantity, therefore, the present invention proposes to describe the error estimation of the state variable by using the elements of the covariance matrix P, specifically using the cross elements of the covariance matrix

To describe the dynamic deformation angular velocity error

(8) And adjusting the size of the F to enable the error of the formula (8) to be as close to the error of the real dynamic deformation angular velocity as possible, thereby improving the effectiveness of error prediction.

To obtain covariance matrix elements

And performing Kalman filtering based on an angular velocity matching equation. The state equation for Kalman filtering is expressed as:

X(k)＝AX(k-1)+W,W～N(0,Q) (9)

k is a positive integer representing a sampling point, X is a state variable, a is called a state transition matrix, and W represents system noise and follows a gaussian distribution with a mean value of zero and a variance of Q.

By dynamic deformation angular velocityInstead of the dynamic deformation angle θ, the state variable is 3 × 3 dimensions:

wherein the content of the first and second substances,

in order to be a static deformation angle,the dynamic deformation angular velocity is shown, and epsilon is the gyro instrument error.

The Kalman filtered measurement equation can be expressed as:

Z(k)＝HX(k)+V,V～N(0,R) (11)

wherein Z represents an observation variable, H represents an observation transfer matrix, and represents the rule that the observation variable changes along with the state quantity. V denotes the measurement noise, which follows a gaussian distribution with mean zero and variance R.

The observed variables are defined as:

the observation variable is the angular velocity vector difference.

The observation transition matrix is defined as:

i is a 3 × 3 identity matrix.

The state transition matrix can be written as:

the state noise is

W＝[0 0 σ_ε]^T(15)

σ_εIs the noise variance of the gyro.

After the state equations and measurement equations are determined, the calculations can be performed using five recursion equations that initiate standard Kalman filtering. With the continuous update of the observation variable z (k), the state variable x (k) can be updated by circularly calculating the five recurrence formulas, and finally, the online real-time detection of the signal is realized:

in formula (16), X^-(k) The estimated value is a priori state estimated value, which is obtained by predicting the information to be measured through a model A of the system before the introduction of measurement information Z (k); p^-(k) For a priori variance, it characterizes the predicted value X^-(k) The error distribution of (2); k (k) is the gain of the system, which characterizes the prediction error P of the system^-(k) The weight of the measurement error R is obtained by using the gain K (k) and the measurement information Z (k), and the posterior state estimated value X (k) is obtained after the measurement error and the prediction error are weighted. P (k) is the a posteriori variance, which characterizes the error distribution of the estimate x (k), i.e. the desired covariance matrix P. Cross element using covariance matrix

Describing dynamic deformation angular velocity error

Calculation by substituting into equation (8)

Will be provided with

Substituting into formula (7) as follows:

the formula is a deformation angle error estimation model containing an optimization coefficient F.

For sequence sampling data with the length of k, a calculation formula of deformation angle measurement errors is as follows:

the invention is realized as follows:

step 1: setting sequence data length k and optimization coefficient F.

The optimization coefficient F can be determined experimentally. In order to ensure the accuracy of the error estimation, there must be sufficient data length. For an object which is periodically modulated by sea waves like a ship, the data length should be at least more than 10 periods and about more than 100 seconds.

Step 2: performing Kalman matched filtering according to the IMU measured value to obtain the cross elements of the covariance matrix

And step 3: calculating the error of each axial component of dynamic deformation angular velocity

The optimization coefficients F determined in the step and the cross elements of the covariance matrix obtained in the stepSubstituting the formula (8) to obtain the error of each axial component of the dynamic deformation angular velocity

Step (ii) of4: calculating the error of each axial component of the deformation measurement

According to angular velocity

The error of each axial component of the dynamic deformation angular velocity measurement calculated in the third step is calculated according to the formula (18) to obtain the error of each component of the angular deformation measurement with k data lengths

And 5: outputting the calculation result

As an estimate of angular deformation measurement error for the inertial mass matching alignment.

The corresponding processing flow diagram is shown in fig. 2.