阅读说明：本技术 一种融合机器视觉和激光参照点信息的目标位姿测量方法 (Target attitude and position measurement method integrating machine vision and laser reference point information ) 是由 张高鹏 彭建伟 梅超 廖加文 任龙 黄继江 于 2021-07-29 设计创作，主要内容包括：本发明属于空间目标位姿测量领域,涉及一种融合机器视觉和激光参照点信息的目标位姿测量方法,应用于空间近场操作及在轨服务中的非合作目标位姿测量过程。克服传统正交迭代算法存在的运算效率较非迭代算法低的问题,利用激光参照点作为单目视觉位姿测量方法的空间特征点,对传统正交迭代算法的中间过程进行整合,通过在迭代过程消除平移向量的中间值来实现正交迭代算法的加速求解,同时利用平行透视投影模型来求解正交迭代算法中的旋转矩阵初始值,使得算法的性能和效率都得到了改善。(The invention belongs to the field of spatial target pose measurement, and relates to a target pose measurement method fusing machine vision and laser reference point information, which is applied to a non-cooperative target pose measurement process in spatial near-field operation and in-orbit service. The method solves the problem that the traditional orthogonal iterative algorithm is lower in operation efficiency than a non-iterative algorithm, integrates the intermediate process of the traditional orthogonal iterative algorithm by using a laser reference point as a spatial characteristic point of a monocular vision pose measurement method, realizes the accelerated solution of the orthogonal iterative algorithm by eliminating the intermediate value of a translation vector in the iterative process, and solves the initial value of a rotation matrix in the orthogonal iterative algorithm by using a parallel perspective projection model, so that the performance and the efficiency of the algorithm are improved.)

1. A target attitude measurement method fusing machine vision and laser reference point information is characterized by comprising the following steps:

step 1, taking a laser reference point as a spatial characteristic point, imaging the laser reference point, and extracting a coordinate of an imaging point of the laser reference point in a camera pixel coordinate system;

step 2, constructing object space collinear errors, and taking the minimum value of the object space collinear errors as a target function to iteratively solve the attitude parameter rotation matrix R;

step 2.1, determining an initial value of a rotation matrix;

step 2.2, determining a sight line projection matrix W of an imaging point of a laser reference point by using a formula 7_i：

Wherein, thereinIs the coordinate of the ith laser reference point in the target coordinate system,homogeneous coordinates of a normalized image point corresponding to the ith laser reference point;

step 2.3, utilizing the sight line projection matrix W_iInitial values of the rotation matrix R andconstruction-side alignment error:

wherein the translation vector is solved using equation 10

Wherein I is an identity matrix;

step 2.4, returning to step 2.3, obtaining the optimal solution of the absolute orientation problem by using a Singular Value Decomposition (SVD) method, and then iteratively updating the rotation matrix R until an iteration termination condition is met;

step 2.5, selecting the minimum object party collinear error obtained in the iterative updating process as an objective function of pose estimation:

translation vectorThe optimal solution of (a) is:

2. a method of target pose measurement fusing machine vision and laser reference point information according to claim 1, characterized by step 2.1 solving the initial value of the rotation matrix using parallel perspective model:

set laser reference point set { P_iThe homogeneous coordinate of (1) is P_i＝(X_i,Y_i,Z_i,1)^TCorresponding set of image points { p_iThe homogeneous coordinate of (i) } is p_i＝(x_i,y_i,1)^TSet of laser reference points { P }_iThe centroid homogeneous coordinate isThe centroid image point homogeneous coordinate is (x)₀,y₀,1)^TThen the initial value R of the rotation matrix is rotated⁰Comprises the following steps:

wherein the content of the first and second substances,andrespectively representAndthe corresponding anti-symmetric matrix is then used,andthree-dimensional column vectors, respectively, the result of which can be determined by:

3. a method of target attitude measurement incorporating machine vision and laser reference point information according to claim 1 or 2, wherein: the step 1 specifically comprises the following steps:

step 1.1, recording the spatial three-dimensional coordinates of the laser reference point;

step 1.2, imaging the laser reference point, and preprocessing the laser reference point imaging picture, wherein the preprocessing mainly comprises color image graying processing, image filtering, histogram equalization, edge sharpening and image denoising processing;

and step 1.3, extracting coordinates of an imaging point of the laser reference point in a camera pixel coordinate system by adopting a Harris angular point extraction algorithm.

4. The method of fusion machine vision and laser reference point information target pose measurement according to claim 3, wherein: step 2 is followed by step 3, based on the orthogonal simulation test, analyzing the measurement accuracy:

step 3.1, designing an orthogonal test;

taking five factors of spatial feature point image coordinate extraction precision, spatial feature point spatial coordinate precision, camera principal point calibration precision, normalized focal length calibration precision and number of spatial feature points as factors influencing measurement precisionA major factor; three typical levels were chosen for each factor, using L₁₈(3⁵) The orthogonal table of (2);

step 3.2, defining the robustness index of the product quality characteristic;

error in pose parameter (Delta A)_x、ΔA_y、ΔA_z、ΔP_x、ΔP_y、ΔP_z) Respectively used as the robustness indexes of the product quality characteristics; wherein Δ A_x、ΔA_y、ΔA_zThe rotation angle errors in the x direction, the y direction and the z direction are respectively; delta P_x、ΔP_y、ΔP_zThe position errors in the x, y and z directions are respectively;

step 3.3, analyzing the signal to noise ratio;

based on L₁₈(3⁵) Establishing 18 groups of simulation tests, and calculating the signal-to-noise ratios of different pose parameter errors by using the results of the 18 groups of simulation tests;

step 3.4, calculating the range of the signal-to-noise ratio;

calculating the signal-to-noise ratios of the parameter errors of different poses calculated in the step 3.3 to obtain extreme differences, wherein the greater the extreme differences are, the higher the influence level of the influence factors is, and the greater the influence is;

step 3.5, calculating the influence ranking of each influence factor on each pose parameter;

based on the extreme difference calculation result in the step 3.4, the influence ranking of each influence factor on each pose parameter is calculated, and the first influence factors influencing the precision of different pose parameters are determined.

Technical Field

The invention belongs to the field of spatial target pose measurement, and particularly relates to a target pose measurement method fusing machine vision and laser reference point information, which is applied to a non-cooperative target pose measurement process in spatial near-field operation and in-orbit service.

Background

The accurate measurement of the relative position and attitude (collectively referred to as pose) of a space target is the key to complete the tasks of space intersection butt joint, attack and defense confrontation, on-orbit capture and maintenance and the like, and the pose measurement method based on monocular vision has the advantages of simple system structure, simple and clear camera calibration steps, wide measurement view field range, low cost, high measurement real-time efficiency and the like compared with binocular and multi-view vision measurement methods. By virtue of the advantages, the pose measurement method based on monocular vision is widely applied to the field of space non-cooperative target pose measurement. Pose measurement methods based on monocular vision can be broadly divided into two major categories: one is to solve pose parameters based on the known geometric shape of the target to be measured, such as a circular ellipse method, a target length-width ratio method and the like. And the other type is a pose solving algorithm based on target characteristic mark information. The former needs to know the specific geometric shape of the target, the latter is not limited by the geometric shape of the target, and is not only suitable for regular targets, but also suitable for various targets with irregular shapes, and in contrast, the latter has higher research and practical values, so the former gradually becomes a research hotspot in the field of pose measurement of monocular vision. The latter can be divided into a monocular vision pose measurement technology based on point characteristics and a monocular vision pose measurement technology based on linear characteristics according to different target characteristic mark information.

The target pose estimation method based on the Point features is also called a Perspective n-Point (PnP), namely, internal parameters of a given camera, coordinate information of n spatial feature points in a target coordinate system and pixel coordinates of corresponding image points of the n spatial feature points in an image coordinate system are given, and then pose information of the target in the camera coordinate system is solved. The PnP problem is classified according to a solving method, and can be classified into a non-iterative method and an iterative method. The most classical non-iterative method is the DLT method, which is initially used for camera calibration and after modification can solve pose information based on at least 4 coplanar feature points or at least 6 non-coplanar feature points. However, the DLT method cannot ensure the orthogonality of the rotation matrix, is very sensitive to noise, and has low robustness. The iteration method generally uses the image surface reprojection error as an objective function, then uses nonlinear optimization algorithms such as a Gauss-Newton method or a Levenberg-Marquardt method to carry out iteration solution, and solves the pose information by minimizing the objective function, so that the accuracy and the robustness are high. However, the method has the disadvantages that the relationship between the pose resolving precision and the initial value of the rotation matrix in the iterative algorithm is large, the iterative algorithm is large in calculation amount, and the algorithm efficiency is low. Aiming at the defect, DeMenthon and the like propose a POSIT (position from the original and Scaling with operations) algorithm, the algorithm obtains an initial value of a rotation matrix by using a weak perspective projection model, and then solves the pose information by using a related iterative algorithm, the POSIT algorithm has high precision, but the obtained rotation matrix is not the optimal rotation matrix. Horaud provides a pose solving method based on parallel perspective iteration, the method replaces a weak perspective projection model with a parallel perspective model, the stability of an algorithm is improved, and better solving speed can be obtained. However, the algorithm also cannot guarantee the orthogonality of the rotation matrix, and other methods are needed to solve the closest orthogonal matrix, but the obtained matrix is often close to the true rotation matrix but still not the optimal rotation matrix. To solve this problem, Lu proposes an orthogonal iterative algorithm (Fast and global converging position estimation from video images "(c.p.lu, g.hager, e.m. johns, IEEE trans. pattern Analysis and Machine Intelligence, vol.22, No.5, pp.610-622, 2000) which takes a target space collinearity error (object side collinearity error) as an objective function and can directly solve an orthogonal rotation matrix, and since the algorithm has the advantages of high precision, good robustness, global convergence and the fact that the algorithm precision does not depend on the initial value of the rotation matrix, the algorithm is gradually one of the research hotspots in the field of pose measurement based on monocular vision, but the method is still an iterative algorithm in nature, which determines that the operation efficiency is necessarily lower than that of a non-iterative algorithm, while for the space of camera facing the space target pose measurement, it requires higher calculation efficiency of the iterative algorithm, and therefore needs to be improved, the operation efficiency is improved.

Disclosure of Invention

In order to solve the problem that the traditional orthogonal iterative algorithm is lower in operation efficiency than a non-iterative algorithm, the invention provides a method for measuring the pose of a spatial non-cooperative target by fusing monocular vision and laser reference point information.

The technical scheme of the invention is to provide a target attitude measurement method integrating machine vision and laser reference point information, which is characterized by comprising the following steps:

step 1, taking a laser reference point as a spatial characteristic point, imaging the laser reference point, and extracting a coordinate of an imaging point of the laser reference point in a camera pixel coordinate system;

step 2, constructing object space collinear errors, and taking the minimum value of the object space collinear errors as a target function to iteratively solve the attitude parameter rotation matrix R;

step 2.1, determining an initial value of a rotation matrix;

step 2.2, determining a sight line projection matrix W of an imaging point of a laser reference point by using a formula 7_i：

Wherein, thereinIs the coordinate of the ith laser reference point in the target coordinate system,homogeneous coordinates of a normalized image point corresponding to the ith laser reference point;

step 2.3, utilizing the sight line projection matrix W_iInitial values of the rotation matrix R andconstruction-side alignment error:

wherein the translation vector is solved using equation 10

Wherein I is an identity matrix;

step 2.4, returning to step 2.3, obtaining the optimal solution of the absolute orientation problem by using a Singular Value Decomposition (SVD) method, and then iteratively updating the rotation matrix R until an iteration termination condition is met;

step 2.5, selecting the minimum object party collinear error obtained in the iterative updating process as an objective function of pose estimation:

translation vectorThe optimal solution of (a) is:

further, step 2.1 solves the initial value of the rotation matrix using a parallel perspective model:

set laser reference point set { P_iThe homogeneous coordinate of (1) is P_i＝(X_i,Y_i,Z_i,1)^TCorresponding set of image points { p_iThe homogeneous coordinate of (the normalized pixel homogeneous coordinate) is p_i＝(x_i,y_i,1)^TSet of laser reference points { P }_iThe centroid homogeneous coordinate isThe centroid image point homogeneous coordinate is (x)₀,y₀,1)^TThen the initial value R of the rotation matrix is rotated⁰Comprises the following steps:

wherein the content of the first and second substances,andrespectively representAndthe corresponding anti-symmetric matrix is then used,andthree-dimensional column vectors, respectively, the result of which can be determined by:

further, step 1 specifically includes the following steps:

step 1.1, recording the spatial three-dimensional coordinates of the laser reference point;

step 1.2, imaging the laser reference point, and preprocessing the laser reference point imaging picture, wherein the preprocessing mainly comprises color image graying processing, image filtering, histogram equalization, edge sharpening and image denoising processing;

and step 1.3, extracting coordinates of an imaging point of the laser reference point in a camera pixel coordinate system by adopting a Harris angular point extraction algorithm.

Further, step 2 is followed by step 3, wherein the measurement accuracy is analyzed based on an orthogonal simulation test:

step 3.1, designing an orthogonal test;

taking five factors of spatial feature point image coordinate extraction precision, spatial feature point spatial coordinate precision, camera principal point calibration precision, normalized focal length calibration precision and the number of spatial feature points as main factors influencing measurement precision; three typical levels were chosen for each factor, using L₁₈(3⁵) The orthogonal table of (2);

step 3.2, defining the robustness index of the product quality characteristic;

error in pose parameter (Delta A)_x、ΔA_y、ΔA_z、ΔP_x、ΔP_y、ΔP_z) Respectively used as the robustness indexes of the product quality characteristics; wherein Δ A_x、ΔA_y、ΔA_zThe rotation angle errors in the x direction, the y direction and the z direction are respectively; delta P_x、ΔP_y、ΔP_zThe position errors in the x, y and z directions are respectively;

step 3.3, analyzing the signal to noise ratio;

based on L₁₈(3⁵) Establishing 18 groups of simulation tests, and calculating the signal-to-noise ratios of different pose parameter errors by using the results of the 18 groups of simulation tests;

step 3.4, calculating the range of the signal-to-noise ratio;

calculating the signal-to-noise ratios of the parameter errors of different poses calculated in the step 3.3 to obtain extreme differences, wherein the greater the extreme differences are, the higher the influence level of the influence factors is, and the greater the influence is;

step 3.5, calculating the influence ranking of each influence factor on each pose parameter;

based on the extreme difference calculation result in the step 3.4, the influence ranking of each influence factor on each pose parameter is calculated, and the first influence factors influencing the precision of different pose parameters are determined.

The invention has the beneficial effects that:

1. the invention utilizes the laser reference point as the space characteristic point in the monocular vision pose measurement method to improve the traditional orthogonal iteration algorithm, and the rotation matrix R and the translation vector are respectively calculated once in each iteration process in the traditional orthogonal iteration algorithmThe improvement is that each iteration process only needs to iterate and update the rotation matrix R, and the translation vector does not need to be solved in each iterationIn other words, only the translation vector needs to be output after the last iterationThe optimal solution of (a). Therefore, the process can be eliminated in the iteration processThe intermediate value of (2) reduces the calculation amount in the iteration process, thereby improving the operation efficiency.

2. The method uses a parallel perspective model to solve the initial value of the rotation matrix. Theoretically, the initial value R of the rotation matrix⁰Optionally selected, however, the initial value R of the rotation matrix⁰The selection of (A) has great influence on the operation efficiency of the algorithm, and the initial value R of the rotation matrix⁰When the selection is improper, the calculation amount of the algorithm is very large and the time is long. Solving rotation matrix initialization through parallel perspective modelAnd the operation efficiency is further improved.

Drawings

FIG. 1 is a flow chart of the method of the present invention;

fig. 2 is a schematic diagram of an orthogonal iterative algorithm.

Detailed Description

In the following, the technical solutions in the embodiments of the present invention will be clearly and completely described with reference to the drawings in the embodiments of the present invention, wherein the drawings are only an embodiment of the present invention and do not limit the present invention in any way, and therefore any simple modification, equivalent change or modification of the above embodiments according to the technical essence of the present invention still falls within the scope of the technical solutions of the present invention.

As shown in fig. 1, the basic work flow of the present invention includes the following steps:

step 1, irradiating a target by using a laser, forming a laser reference point on the surface of the target, imaging the laser reference point by using the laser reference point as a spatial characteristic point, and extracting the coordinate of the imaged point of the laser reference point in a camera pixel coordinate system by adopting a Harris angular point extraction algorithm.

1.1, firstly, recording a spatial three-dimensional coordinate of a laser reference point;

and step 1.2, preprocessing the laser reference point imaging photo, wherein the preprocessing mainly comprises color image graying processing, image filtering, histogram equalization, edge sharpening and image denoising processing.

And step 1.3, carrying out corner detection by adopting a Harris corner extraction algorithm, and extracting image pixel coordinates of an imaging point of each laser reference point in an image.

And 2, constructing object space collinear errors, and taking the minimum value of the object space collinear errors as a target function to iteratively solve the attitude parameter rotation matrix.

And 2.1, solving an initial value of the rotation matrix by using a parallel perspective model.

Theoretically, the initial value R of the rotation matrix⁰Optionally selected, however, the initial value R of the rotation matrix⁰Influence of selection on the operating efficiency of the algorithmMaximum, rotation matrix initial value R⁰When the selection is improper, the calculation amount of the algorithm is very large and the time is long. In the method, a parallel perspective model is used for solving the initial value of the rotation matrix.

Under a parallel perspective model, the projection process is divided into two steps: the first step is to project the object parallel to a plane that passes through the centroid and is parallel to the image plane, but the projected line is not parallel to the optical axis but parallel to the line connecting the optical center of the camera and the centroid. The parallel perspective model can be expressed as:

wherein (X)₀,Y₀,Z₀) Are coordinates of the center of mass. The matrix representation of the parallel perspective model is:

wherein

Referred to as a parallel perspective projection matrix.

Let the actual coordinate of the three-dimensional space coordinate P be (X, Y, Z)^T＝(X₀+ΔX,Y₀+ΔY,Z₀+ΔZ)^TParallel perspective model imaging error I_errCan be obtained from the taylor equation:

the equation (4) shows that the imaging error of the parallel perspective model is second-order infinitesimal of the three-dimensional point coordinates. And the image point error under the amblyopia model is the first order infinitesimal of the three-dimensional point coordinates. Therefore, in the present invention, the solution of the initial value of the rotation matrix is performed using a parallel perspective model.

Let three-dimensional space point set { P_iThe homogeneous coordinate of (1) is P_i＝(X_i,Y_i,Z_i,1)^TCorresponding set of image points { p_iThe homogeneous coordinate of (i) } is p_i＝(x_i,y_i,1)^TSet of three-dimensional spatial points { P }_iThe centroid homogeneous coordinate isThe centroid image point homogeneous coordinate is (x)₀,y₀,1)^TThen rotate the initial value R of the matrix⁰Comprises the following steps:

wherein the content of the first and second substances,andrespectively representAnda corresponding antisymmetric matrix.Andthree-dimensional column vectors, respectively, the result of which can be determined by:

thus, the initial value R of the rotation matrix in the orthogonal iterative algorithm can be obtained by the formula (6)⁰。

Step 2.2Assuming that n laser reference points exist in the target coordinate system, wherein the coordinate of the ith laser reference point in the target coordinate system isCorresponding normalized image point homogeneous coordinates ofThe sight line projection matrix of the image point is:

wherein, W_iReferred to as a line-of-sight projection matrix, line-of-sight refers to a ray from the optical center to an image point. And after the laser reference point is acted by the sight line projection matrix, the projection point of the laser reference point on the sight line of the corresponding image point is obtained.

Step 2.3, constructing object space collinear error;

the basic principle of the orthonormal iterative algorithm is that the spatial feature point should coincide with its projection point on the sight line of the corresponding image point, wherein the relationship can be described by a target space collinearity equation:

wherein R andnamely the pose of the camera under a target coordinate system, R is a rotation matrix,is a translation vector.

From equation (8), object-side alignment errors can be constructed:

the inventionSolving translation vector in equation 9 using equation 10

Where I is the identity matrix.

Step 2.4, returning to step 2.3, obtaining the optimal solution of the absolute orientation problem by using a Singular Value Decomposition (SVD) method, and then iteratively updating R until an iteration termination condition is met, as shown in FIG. 2; the iteration end condition in this embodiment is set such that the relative variation amount of the object-side collinear error is smaller than a threshold value set in advance. Specifically, in the present embodiment, if the relative variation of the corresponding object-side collinear error in five consecutive iterations is smaller than 0.001mm, it means that the iterations have stabilized, and the whole iteration process is terminated.

Step 2.5, based on the formula (9) in the iterative process, an objective function of attitude estimation can be obtained:

for equation (11), if the rotation matrix R is known, the vector is translatedThe optimal solution of (a) is:

this is a univariate minimization optimization problem. Can be solved by using an iterative methodThe optimum value of (c). The initial value of the iterative optimization is R⁰Updating R by obtaining the optimal solution to the absolute orientation problem using the singular value decomposition method (SVD), such a processCan finish R andcontinuously iterating and optimizing.

The iteration process of each time of the traditional orthogonal iteration algorithm needs to calculate a rotation matrix R and a translational vector respectivelyIn practice, however, after each R update, the optimum can be solved linearlyThus, each iteration is actually an iteration of the rotation matrix R, and it is not necessary to solve for the translation vector in each iterationIn other words, only the translation vector needs to be output after the last iterationThe optimal solution of (a). Therefore, the present invention can eliminate the interference in the iterative processThe intermediate value of (2) reduces the calculation amount in the iteration process, thereby improving the operation efficiency.

And 3, carrying out quantitative analysis on the accuracy of the pose measurement method based on an orthogonal simulation test.

And 3.1, designing an orthogonal test.

The Tiankou method is created by Tiankou Xuani, a famous quality management expert in Japan, and the Tiankou method enables the functions and the performance of the product to be insensitive to the cause of deviation by adjusting design parameters so as to improve the anti-interference capability of the product. To quantitatively describe the product quality loss, the Tankou proposes the concept of "quality loss function" and measures the robustness of the design parameters by the signal-to-noise ratio. The Tiankou method emphasizes that the design of products must pass through three stages of system design, parameter design and tolerance design, the parameter design is the core process, and the method is mainly characterized in that a quality loss function is introduced and converted into a signal-to-noise ratio, the optimal level combination of each parameter value is found out on the basis of orthogonal experimental design through statistical analysis of an experimental scheme, and therefore the performance and the quality of the products are improved. Because the orthogonal experiment has the characteristics of uniform dispersion and order comparability, the orthogonal table is applied to arrange the experiment to be representative, and the approximate condition of the influence of each level of each factor on the index can be comprehensively reflected.

TABLE 1 numbering and leveling of the geometric factors

The invention takes the thought of the Taguchi method and the result of simulation analysis as the basis, and quantitatively researches the influence of the extraction precision of the image coordinate of the spatial characteristic point, the spatial coordinate precision of the spatial characteristic point, the calibration precision of the camera principal point, the calibration precision of the normalized focal length and the number of the spatial characteristic points on the final pose measurement result by reasonably designing orthogonal experiments. The level numbers of the factors are shown in table 1, each factor has three typical levels, and if each combination is calculated, the total number of the levels is 3⁵Calculating one by one as 243 different combinations would be a very time consuming task, as shown in table 2, using L in the present invention₁₈(3⁵) Only 18 combinations need to be calculated, thereby greatly accelerating the analysis process.

TABLE 2L₁₈(3⁵) Orthogonal table

And 3.2, defining the robustness index of the product quality characteristic.

For the problem of pose measurement of a spatial object, the smaller the error of the pose measurement result, the better, and therefore, in the present invention, the error (Δ a) of the pose measurement result is taken_x、ΔA_y、ΔA_z、ΔP_x、ΔP_y、ΔP_z) Respectively as the robustness indexes of the product quality characteristics (namely the target function of the algorithm precision quantitative analysis).

And 3.3, analyzing the signal to noise ratio.

The Tankou method measures the stability of product quality by the signal-to-noise ratio (SNR). The analysis process is to use an orthogonal test table, and the signal-to-noise ratio is used as an evaluation index of the product robustness, so that researchers can be helped to find out which level of influence is more effective for each control factor. The snr analysis process is an evaluation index of product robustness with snr by using an orthogonal test table to help researchers find which level of influence is more effective for each control factor. In the present invention, 18 sets of simulation experiments were established based on table 2, and the results of the 18 sets of simulation experiments are shown in table 3.

Table 3 results of simulation experiment

And calculating the signal-to-noise ratios of different pose parameter errors based on the 18 sets of simulation test results shown in the table 3. The following is a calculation of Δ P_zSNR of_ΔPzThe calculation of the signal-to-noise ratio is illustrated as an example.

ΔP_zThe signal-to-noise ratio (S/N) can be derived from the following equation:

where n represents the number of times the test was repeated. Since the result of the simulation test is itself the mean square of 100 tests, n is taken to be 1. Based on the formula (13), Δ P in 18 sets of simulation experiments was obtained_zSNR of_ΔPzResults are shown in the last column of Table 4, other pose parameter errors (Δ A)_x、ΔA_y、ΔA_z、ΔP_x、ΔP_y) The signal to noise ratio of (c) can be similarly obtained, and the results are also shown in table 4.

TABLE 4 SNR for each pose parameter error

And 3.4, calculating the extreme difference of the signal to noise ratio. And 3.3, calculating the signal-to-noise ratios of the different pose parameter errors calculated in the step 3.3, wherein the greater the range is, the higher the influence level of the influence factor is, and the greater the influence is.

Specifically, T is shown in Table 5₁The first number of rows is the sum of the signal-to-noise ratios for the 6 sets of trials when the a factor is at the first level. Can obtain T in the same way₁-T₃Other numbers are listed. The very poor signal-to-noise ratio is denoted T₁-T₃The larger the difference between the medium maximum and minimum values, the higher the level of influence of the factor.

TABLE 5 parameter pairs Δ P_zAnalysis of the contribution ratio of

And 3.5, calculating the influence ranking of each influence factor. And 3.4, calculating the influence ranking of each influence factor based on the extreme difference calculation result in the step 3.4, and determining the first influence factors influencing the precision of different pose parameters.

The influence contribution rate and the ranking of each geometric factor are obtained according to the following method:

R_i＝maxT_j-minT_j(j＝1,2,3)(14)

the same method is used for measuring errors (delta A) of other five poses_x、ΔA_y、ΔA_z、ΔP_x、ΔP_y) The influence of the signal-to-noise ratio and various factors on the signal-to-noise ratio is calculated, and the calculation processes are similar and are not repeated herein.

According to the accuracy quantitative calculation method for the pose measurement algorithm, the primary factors influencing each pose parameter can be determined, and the pose measurement result can be optimized in a targeted manner according to the requirements of different space pose measurement tasks.