CN112199814B - System error self-checking method, device, equipment and medium for measuring system - Google Patents
System error self-checking method, device, equipment and medium for measuring system Download PDFInfo
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Abstract
The method comprises the steps of constructing a system error self-checking model based on Gauss-Helmert and considering random errors, obtaining an initial value of an unknown parameter vector, an initial value of a random error vector and an observed value of a homonymy point in the model, iteratively solving the unknown parameter vector and the random error vector by adopting a nonlinear least square theory and a Newton-Gaussian method, and obtaining a final solution value of the unknown parameter vector meeting a preset convergence condition, so that the system error parameter of the measuring system is obtained, and the solving precision of the system error parameter in the measuring system is effectively improved; in addition, the method can realize posterior estimation under the condition of wrong prior information or unknown prior information by a variance component estimation method, and effectively ensures the solving precision of system error parameters.
Description
Technical Field
The invention relates to a calibration method of a measurement system, in particular to a system error self-checking method, a device, equipment and a medium of the measurement system based on a Gauss-Helmert model and considering random error information.
Background
The ground three-dimensional Laser Scanner (TLS) technology is widely used in various fields as a measurement technology for rapidly and accurately acquiring object space information. However, in the process of acquiring point cloud data by using the TLS technique, due to the influence of many factors such as the accuracy of the apparatus itself, the external environment, and the scanning target, a system error of the measurement system and a random error of measurement are superimposed on the point cloud coordinate information, so that the obtained point cloud coordinate is inconsistent with the actual coordinate of the target point. Therefore, in order to ensure the observation accuracy of the point cloud coordinates, the observation values of the point cloud coordinates need to be calibrated.
The self-checking method is a TLS checking method widely applied at present, and can be used for solving system errors by taking possible system errors as undetermined parameters to participate in the overall adjustment operation. Compared with the traditional calibration method, the method can greatly reduce the requirements on the measurement environment and operators. At present, a common point-based self-calibration method does not consider random error information when a function model is constructed; therefore, when the TLS self-checking is performed by using such a function model, it is difficult to avoid the influence of random errors in the observed values on the calculation accuracy of the system error parameters, which causes the system error not to correspond to the real error, and thus the accuracy of parameter calculation cannot be ensured.
Disclosure of Invention
In view of the above disadvantages in the prior art, an object of the present invention is to provide a method, an apparatus, a device, and a computer storage medium for self-checking and calibrating a system error of a measurement system, which are used to solve the problems that a random error in an observed value affects the calculation accuracy of a system error parameter, so that the system error does not correspond to a real error, and the accuracy of parameter calculation cannot be ensured.
To achieve the above and other related objects, the present invention provides a method for self-checking a system error of a measurement system, the method comprising:
constructing a first system error self-checking model based on Gauss-Helmert and considering random errors, and determining an unknown parameter vector and a random error vector of the first system error self-checking model; determining a corresponding target function based on the first system error self-checking model; wherein the unknown parameter vector comprises an external conversion parameter and a calibration parameter; acquiring an initial value of the unknown parameter vector, an initial value of the random error variable and an original observed value of a homonymy point; based on the initial value of the unknown parameter vector, the initial value of the random error vector and the original observed value, performing iterative solution of the unknown parameter vector and the random error vector on the first system error self-checking model by adopting a Newton-Gaussian method of nonlinear least squares to obtain a final solution value of the unknown parameter vector meeting a preset convergence condition; the final solution value of the unknown parameter vector comprises a system error value of the measurement system.
In an embodiment of the present invention, the method for self-calibrating a system error of the measurement system further includes: and optimizing the iterative solution process by adopting a variance component estimation method in the iterative solution process of the unknown parameter vector and the random error vector of the first system error self-calibration model by adopting a non-linear least square Newton-Gaussian method based on the initial value of the unknown parameter vector, the initial value of the random error vector and the original observed value, so as to obtain the solution value of the unknown parameter which is optimized and meets the preset convergence condition.
In an embodiment of the present invention, the constructing a system model based on Gauss-Helmert and considering random error information includes: determining a random error vector; and constructing the first system error self-checking model based on the random error vector, wherein the first system error self-checking model is a function model of the reference coordinate of the observation point relative to the original observation coordinate, the rotation parameter, the checking error parameter and the random error vector of the observation point.
In an embodiment of the present invention, the iterative solution of the unknown parameter vector and the random error vector to the first system error self-calibration model based on the initial value of the unknown parameter vector, the initial value of the random error vector, and the original observed value by using a newton-gaussian method of nonlinear least squares includes: performing binary Taylor series expansion on the first system error self-checking model at the initial iteration value of the unknown parameter vector and the initial iteration value of the random error vector to obtain a second system error self-checking model; constructing a Lagrange objective function by using the objective function and the second system error self-checking model, and resolving to obtain resolving values of the unknown parameter vector and the random error vector according to Lagrange requirements; judging whether the calculation value of the unknown parameter vector meets the preset convergence condition, if so, exiting the iterative calculation process, and taking the calculation value as the final calculation value of the unknown parameter vector to obtain a system error value of the measurement system; otherwise, obtaining a solution value of the unknown parameter vector and a solution value of the random error vector, respectively replacing the solution values with an iteration initial value of the unknown parameter vector and an iteration initial value of the random error vector, and repeatedly executing the iteration solution.
In an embodiment of the present invention, the obtaining an initial iteration value of the unknown parameter vector includes: and solving the initial value of the external conversion parameter in the unknown parameter vector by using a linear Gaussian Markov model, and taking a zero matrix as the initial value of the calibration parameter.
In an embodiment of the present invention, the optimizing the iterative solution process by using a variance component estimation method to obtain the optimized solution value of the unknown parameter vector that satisfies the preset convergence condition includes: performing observation value classification on the original observation value; and adjusting the random error weight matrix according to the observed values in a classified manner to obtain an optimized random error weight matrix, replacing the optimized random error weight matrix with the random error weight matrix in the second system error self-checking model, and executing the iterative calculation process to obtain a calculated value of the unknown parameter vector which satisfies the preset convergence condition after optimization.
The invention also provides a system error self-checking device of the measuring system, which comprises: the model construction module is used for constructing a first system error self-checking model based on Gauss-Helmert and considering random errors, and determining an unknown parameter vector and a random error vector of the first system error self-checking model; determining a corresponding target function based on the first system error self-checking model; the unknown parameter vector comprises an external conversion parameter and a calibration parameter; the system initial value module is used for acquiring an initial value of the unknown parameter vector, an initial value of the random error variable and an original observed value of the same-name point; the iterative calculation module is used for carrying out iterative calculation on the unknown parameter vector and the random error vector on the first system error self-checking model by adopting a non-linear least square Newton-Gaussian method based on the initial value of the unknown parameter vector, the initial value of the random error vector and the original observed value so as to obtain a final solution value of the unknown parameter vector meeting a preset convergence condition; the final solution value of the unknown parameter vector comprises a system error value of the measurement system.
In an embodiment of the invention, the model building module includes: a random error vector submodule for determining a random error vector; and the first system model submodule is used for constructing the first system error self-checking model based on the random error vector, and is a function model of the reference coordinate of the observation point about the original observation coordinate, the rotation parameter, the checking error parameter and the random error vector.
In an embodiment of the invention, the iterative solution module includes: the linear conversion submodule is used for performing binary Taylor series expansion on the first system error self-checking model at the initial iteration value of the unknown parameter vector and the initial iteration value of the random error vector to obtain a second system error self-checking model; the parameter calculation submodule is used for constructing a Lagrangian target function by using the target function and the second system error self-checking model, and calculating to obtain calculation values of the unknown parameter vector and the random error vector according to Lagrangian necessary conditions; the parameter determination iteration submodule is used for determining whether a calculation value of the unknown parameter vector meets the preset convergence condition, if so, the iteration calculation process is exited, and the calculation value is used as a final calculation value of the unknown parameter vector to obtain a system error value of the measurement system; otherwise, the solution value of the unknown parameter vector and the solution value of the random error vector are obtained and are respectively replaced by the initial iteration value of the unknown parameter vector and the initial iteration value of the random error vector, and the iteration solution module is repeatedly executed.
In an embodiment of the invention, the apparatus further includes: and the optimization submodule is used for optimizing the iterative calculation process by adopting a variance component estimation method in the process of executing the iterative calculation module program to obtain the optimized calculation value of the unknown parameter meeting the preset convergence condition.
In an embodiment of the present invention, the optimization submodule is configured to execute, and includes: carrying out observation value classification on the original observation value; and adjusting the random error weight matrix according to the observed values in a classified manner to obtain an optimized random error weight matrix, replacing the random error weight matrix in the second system error self-checking model with the optimized random error weight matrix, and executing a program of the iterative solution module to obtain a solution of the unknown parameter vector which satisfies the preset convergence condition after optimization.
The present invention also provides an electronic device, comprising: a processor and a memory; the memory is used for storing computer programs, and the processor is used for executing the computer programs stored by the memory so as to enable the electronic equipment to execute the steps in the system error self-checking method of the measuring system.
In addition, the present invention also provides a computer storage medium, which stores a computer program that, when executed by a processor, implements the steps in the system error self-checking method of the measurement system.
As described above, according to the method, the device, the equipment and the computer storage medium for self-checking of the system error of the measurement system provided by the invention, the system error parameter of the measurement system is obtained by constructing the system model based on Gauss-helper and taking random errors into consideration and calculating the system model added with random error information, so that the calculation accuracy of the system error parameter in the measurement system can be effectively improved; in addition, the method can also realize a post-test estimation method through variance component estimation under the condition of error of prior information or unknown prior information, and effectively ensures the solving precision of system error parameters.
Drawings
FIG. 1 is a flow chart of a system error self-calibration method of a measurement system according to an embodiment of the present invention
A schematic view;
FIG. 2 is a flow chart illustrating a single iterative solution process according to an embodiment of the present invention;
FIG. 3 shows the estimates of the parameters for 3 different experimental protocols in the first scenario in one embodiment
The sequence of difference values with the true value of the parameter and the RMSE thereof;
FIG. 4 shows the coordinate component errors for 3 different experimental scenarios in the first scenario in one embodiment
And a point location error;
FIG. 5 shows the estimates of the parameters for 3 different experimental protocols in the second scenario in one embodiment
The sequence of difference values with the true value of the parameter and the RMSE thereof;
FIG. 6 shows the coordinate component errors for 3 different experimental scenarios in the first scenario in one embodiment
And a point location error;
FIG. 7 shows the estimates of the parameters for 3 different experimental protocols in a third scenario in one embodiment
The sequence of difference values with the true value of the parameter and the RMSE thereof;
FIG. 8 shows the coordinate component errors for 3 different experimental scenarios in a third scenario in one embodiment
And a point location error;
FIG. 9 shows the difference between the absolute values of the correlation coefficients of case 4 and case 5 in one embodiment;
fig. 10 is a schematic structural diagram of a system error self-calibration apparatus of the measurement system according to an embodiment of the invention.
Description of the element reference numerals
1. Model building module
11. Random error vector submodule
12. First system model submodule
2. System initial value module
3. Iterative solution module
31. Linear conversion submodule
32. Parameter resolving submodule
33. Parameter decision iteration submodule
34. Optimization submodule
S100-S300 steps
S302-S306 steps
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It is to be noted that the features in the following embodiments and examples may be combined with each other without conflict.
It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention, and the components related to the present invention are only shown in the drawings rather than drawn according to the number, shape and size of the components in actual implementation, and the type, quantity and proportion of the components in actual implementation may be changed freely, and the layout of the components may be more complicated.
Example 1
Please refer to fig. 1, which is a schematic structural diagram of a system error self-calibration method of a measurement system according to an embodiment 1 of the present invention.
As shown in fig. 1, the implementation of the method comprises the following steps:
s100, constructing a first system error self-checking model based on Gauss-Helmert and considering random errors, and determining unknown parameter vectors and random error vectors of the first system error self-checking model; and determining a corresponding objective function based on the first system error self-checking model.
Specifically, based on the Gauss-helle model, a first system error self-checking model considering random errors is constructed, and the method comprises the following steps:
1) Determining a random error vector;
according to the observation principle of the measurement system, the original observation values of the observation points comprise distances, vertical angles and horizontal angles. Therefore, according to the error distribution rule of the measurement system, the random error vector of the observation point is determined as follows:
wherein e represents a random error vector;
e s ,e θ ,e α random errors of distance, vertical angle and horizontal angle respectively;
σ s ,σ θ ,σ α respectively the middle error of the random error of the distance, the random error of the vertical angle and the random error of the horizontal angle;
compliance is represented.
2) Based on the random error vector, constructing the first system error self-checking model, which is a function model of the reference coordinate of the observation point about the original observation coordinate, the rotation parameter, the checking error parameter and the random error vector of the observation point, and comprises the following steps:
wherein, X, Y and Z are reference coordinates of the observation point, namely reference coordinates of X, Y and Z axes; the reference coordinate is a three-dimensional coordinate of an observation point measured by a high-precision instrument (such as a high-precision total station), and the three-dimensional coordinate is generally considered to contain no error;
s, theta, alpha are original observation coordinates of the observation point and are spherical coordinate values, and respectively represent the distance from the observation point to the measurement origin, the vertical angle of the observation direction and the horizontal angle of the observation direction; the original observation coordinate is a three-dimensional coordinate of an observation point measured by the measuring system, and an original observation value of the observation point is obtained after inverse calculation is carried out on the three-dimensional coordinate;
r is a rotation parameter matrix composed of rotation parameters
A matrix of ω, κ, wherein
Is the rotation angle of the Y axis, omega is the rotation angle of the X axis, and kappa is the rotation angle of the Z axis;
m, λ, c ', i', t are calibration Parameters and also Additional Parameters (APs); wherein m is an addition constant, lambda is a multiplication constant, c 'is a sight axis related error, i' is a horizontal axis related error, and t is a vertical angle index difference;
Δ X, Δ Y, Δ Z represent translation parameters in the X, Y, Z axes, respectively.
3) Determining an unknown parameter vector corresponding to the first system error self-checking model;
comprises the following steps:
the unknown parameter vector comprises the external conversion parameter and the calibration parameter;
wherein, Δ x, Δ y, Δ z,
ω, κ is the External transformation parameter (EOPs);
m, λ, c ', i', t are the calibration Parameters (APs).
In this embodiment, a corresponding objective function is determined according to the first system error self-calibration model; the objective function is a least squares function with respect to the random error vector and a random error weight matrix;
the objective function is:
e T Pe＝min (4)
where P is the random error weight matrix.
S200, acquiring an initial value of the unknown parameter vector, an initial value of the random error variable and an original observed value of a homonymy point;
let xi be the initial value of xi 0 Namely:
let e have an initial value of e 0 ；e 0 Equal to 0, i.e.;
in this embodiment, for the external transformation parameters, solving initial values of the external transformation parameters in the unknown parameter vector by using a linear Gauss-Markov model;
for the initial values of the calibration parameters, the instrument is generally considered to have eliminated various errors after being shipped from the factory, and therefore, the initial values of the calibration parameters are zero matrixes, that is, each element in the matrixes is 0.
And S300, based on the initial value of the unknown parameter vector, the initial value of the random error vector and the original observed value, performing iterative solution on the unknown parameter vector and the random error vector by the first system error self-calibration model by adopting a non-linear least square Newton-Gaussian method to obtain a final solution value of the unknown parameter vector meeting a preset convergence condition.
And the calibration parameter value in the final solution value of the unknown parameter vector is a system error value of the measurement system.
In this embodiment, the process of a single iterative solution includes:
s302, performing binary Taylor series expansion on the first system error self-checking model at the initial iteration value of the unknown parameter vector and the initial iteration value of the random error vector to obtain a second system error self-checking model;
and the second system error self-checking model is the first system error self-checking model after linear conversion.
The initial iteration value of the unknown parameter vector is the value of the unknown parameter vector obtained by executing the previous iteration calculation process in the current iteration calculation process; similarly, the initial value of the random error vector is a value of the random error vector obtained by executing the previous iterative solution process in the current iterative solution process.
For example, in the j-th iterative solution process, the initial iterative value of the unknown parameter vector is a solution value of the unknown parameter vector obtained by performing the iterative solution for the j-1 th time; the initial iteration value of the random error vector is a resolving value of the random error vector obtained by executing the iterative resolving for the j-1 th time. When j is 1, the initial iteration value of the unknown parameter vector is equal to the initial value of the unknown parameter vector, and the initial iteration value of the random error vector is equal to the initial value of the random error vector, that is:
when the j =1, the current value of the current is set to be equal to or less than 1,
wherein ξ j An iteration initial value of the unknown parameter vector in the jth iteration resolving process;
e j and in the j-th iterative calculation process, the initial iterative value of the random error vector is obtained.
The first system error self-checking model is substantially a nonlinear equation, so that the unknown parameters are difficult to directly solve by adopting methods such as least squares and the like; therefore, the model needs to be linearly converted first.
Specifically, to simplify the calculation, the observation vector of the observation point is first made to be:
substituting the equation 8 into the first system error self-checking model (equation 2), that is:
specifically, the right element of formula 9 is positioned in the iteration initial value ξ of the unknown parameter vector by adopting a binary taylor series j And an initial value e of the iteration of the random error variable j And (3) unfolding to obtain the second system error self-checking model, which is as follows:
in the formula 10, the process is described,
are respectively shown in formula 10
The coefficient matrices for ω and κ, respectively, are:
the superscript j is the sequence number of the iterative solution, namely represents the jth iterative solution process;
e cj for the j iteration resolving, the randomA calculated value of the error vector;
e cj -e j and the error vector is the residual error vector of the random error, namely the difference value between the calculation value of the random error vector and the initial iteration value of the random error vector in the j iteration calculation.
To further simplify the calculation, let:
in formula 10, the coefficient matrix of each parameter in the calibration parameter vector is respectively expressed as:
since the equation 10 is a non-linear model, as in the parametric solution, it is necessary to calculate the partial derivative for each element in the residual vector of the random error.
Order:
correspondingly, the partial derivative of the observation coordinate H of the observation point with respect to de is:
in the formula
γ＝c·secθ j ·tanθ j +i·sec 2 θ j (16)
For the convenience of understanding and calculation, the second systematic error self-checking model is expressed in a simplified manner, that is, the same terms in the second systematic error self-checking model (formula 10) are combined to obtain,
wherein, A j A coefficient matrix representing the unknown parameter vector is:
in the formula, E 3×3 Is a 3-dimensional identity matrix;
in the formula, d ξ is a residual vector of the unknown parameter vector, and is a variation between a solution value of the unknown parameter vector in the current iteration solution and the initial iteration value, and is expressed as follows:
wherein d Δ x, d Δ y, d Δ z,
d ω, d κ, dm, d λ, dc, di, dt are residual variables of the unknown parameters, respectively.
S304, constructing a Lagrange objective function by using the objective function and the second system error self-checking model, and resolving to obtain resolving values of the unknown parameter vector and the random error vector according to Lagrange requirements;
specifically, based on the second system error self-calibration model and the objective function, a lagrangian objective function is constructed, which is:
Φ＝e T Pe+2K T (L j -A j dξ-B j de)＝min (20)
in the formula (I), the compound is shown in the specification,
wherein K is a Lagrangian multiplier;
B j calculating a coefficient matrix of the random error vector in the jth iteration;
the weight matrix P of the random error vector is represented as:
wherein q is ∈ [1, n ]](ii) a n represents the total number of homologous points; sigma s ,σ θ ,σ α Respectively, the median error of the distance, the vertical angle and the horizontal angle, which are prior information, can be obtained from the nominal accuracy. The nominal precision is a medium error value of the measuring system provided when the measuring system leaves a factory.
Based on the constructed lagrangian objective function (formula 20), a solution of the formula is obtained through Euler-Lagrange requirements, that is, the partial derivative of each variable in the formula 20 is made to be zero, so as to obtain an estimated value of the residual vector of the unknown parameter and an estimated value of the random error vector of the observed value in the j iteration calculation, as follows:
wherein the content of the first and second substances,
is d xi j Is determined by the estimated value of (c),
is e cj An estimated value of (d); q is a co-factor matrix of observations, Q c Is a co-factor matrix of parameters and satisfies:
taking the estimation value of the random error vector as a resolving value of the random error vector; superposing the initial value of the unknown parameter vector with the estimated value of the residual vector of the unknown parameter obtained after calculation to obtain the calculated value of the unknown parameter vector, namely:
s306, judging whether the calculation value of the unknown parameter vector meets the preset convergence condition, if so, exiting the iterative calculation process, and taking the calculation value as the final calculation value of the unknown parameter vector to obtain a system error value of the measurement system; otherwise, the solution value of the unknown parameter vector and the solution value of the random error vector are obtained and are respectively replaced by the initial iteration value of the unknown parameter vector and the initial iteration value of the random error vector, and the step S302 is returned;
in this embodiment, the predetermined convergence condition includes that the translation parameter of the external transformation parameters is less than 10 -7 m, and said rotation parameter of said external conversion parameters is less than 0.0001 °.
Specifically, the calculated value of the unknown parameter vector obtained by calculation is compared with the preset convergence condition,
when the preset convergence condition is not met in the calculation values of the unknown parameter vectors obtained by iterative calculation, the calculation values of the unknown parameter vectors are obtained to be used as the initial iteration values of the unknown parameter vectors in the next iterative calculation, the calculation values of the random error vectors are used as the initial iteration values of the random error vectors in the next iterative calculation, the step S302 is returned to execute the next iterative calculation process, and the step is repeated until the calculation values of the unknown parameter vectors obtained by calculation all meet the preset convergence condition.
For example, if there is a solution value of each unknown parameter vector that does not satisfy the preset convergence condition in the j-th iterative solution, the solution value of the unknown parameter vector obtained in the j-th iterative solution is obtained as an initial iteration value of the unknown parameter vector in the j + 1-th iterative solution, and the solution value of the random error vector is used as an initial iteration value of the random error vector in the j + 1-th iterative solution, that is:
returning to step S302 to execute the j +1 times of iterative solution process; and repeating the steps until the resolving values of the unknown parameter vectors obtained by resolving all meet the preset convergence condition.
When the calculated values of the unknown parameter vectors obtained through calculation meet the preset convergence condition, the iterative calculation process is exited, and the calculated values of the unknown parameter vectors are used as final calculated values of the unknown parameter vectors; wherein the calibration parameter in the final solution of the unknown parameter vector is the system error value of the measurement system,
it should be noted that in each iterative calculation process, the coefficient matrix of each unknown parameter in the second system error self-calibration model needs to be updated according to the updated initial iteration value of the unknown parameter vector.
Since the actual precision of the original observed value of the observed point is often not equal to the nominal value, that is, the weight given by the observed value during the first adjustment is not appropriate, the accuracy of the calculation result of the unknown parameter is affected.
Therefore, in order to improve the accuracy of the solution result of the unknown parameter, in this embodiment, the method for self-calibrating the system error of the measurement system further includes, between steps S304 and S306:
s305, optimizing the iterative solution process of the unknown parameter vector and the random error vector by using a variance component estimation method in the iterative solution process of the unknown parameter vector and the random error vector of the first system error self-calibration model by using a non-linear least square Newton-Gaussian method based on the initial value of the unknown parameter vector, the initial value of the random error vector and the original observed value, and obtaining the solution value of the unknown parameter which is optimized and meets the preset convergence condition.
Specifically, the implementation step of optimizing the iterative solution process of the unknown parameter and the random error vector by using a variance component estimation method to obtain the solution value of the unknown parameter vector that is optimized and satisfies the preset convergence condition includes:
1) Carrying out observation value classification on the original observation value according to the observation value type;
in this embodiment, the original observation value of the observation point is divided into a distance, a vertical angle, and a horizontal angle according to the type of the observation value.
2) Classifying and adjusting the random error weight matrix according to the observed values to obtain an optimized random error weight matrix;
specifically, the random error weight matrix is adjusted to be:
wherein E is n×n An identity matrix of dimension n;
according to the functional expression (formula 8) of the observation vector, in the iterative solution process of adjusting the qth homonym point, the partial differential of the observation value vector is:
wherein, the first and the second end of the pipe are connected with each other,
and q is the sequence number of the iterative solution, and the partial differential of each observation value vector in the iterative solution process from the 1 st to the nth homonymous point is converted into a matrix form, wherein the partial differential is as follows:
by adjusting the weight matrix of the random error vector, and the order of the observation vectors, equation 31 is transformed into a new form, which is:
3) And replacing the random error weight matrix in the second system error self-checking model with the adjusted random error weight matrix, and executing the iterative solution to obtain the optimized solution value of the unknown parameter vector meeting the preset convergence condition.
In order to verify the beneficial effect of the system error self-checking and correcting method of the measuring system provided by the invention, verification is carried out in a comparison test mode. The test idea is that a high-precision total station and a scanner are adopted to calibrate points at specified positions respectively to obtain observation data. For two sets of acquired coordinate data, the total station data is assumed to be taken as reference coordinates, namely, the total station data does not contain any system error or random error, the invention and other system error self-checking methods in the prior art are adopted to respectively carry out system error self-checking and correction on the same simulation test data, and the external conversion parameters EOPs and the checking and correcting parameters APs of the measuring system are calculated and acquired.
The following three schemes are adopted to carry out the system error self-checking and correcting of the measuring system.
Scheme 1: non-linear least squares without taking systematic errors into account.
Scheme 2: and (3) a calibration method based on a nonlinear least square method ignores random errors.
Scheme 3: based on the method of the invention.
Aiming at the condition that the prior information and the real precision are often different or the prior information is unknown in the actual measurement environment, the experiment is carried out in 3 situations (3 Cases). The 1 st case is where the nominal accuracy is equal to the true accuracy, while the 2 nd and 3 rd cases are equal weight processing where the distributions of the two pieces of information are slightly different and the a priori information is unknown, respectively. The calculation results are shown in table 1 below and fig. 3 to 8.
Wherein, fig. 3, fig. 5 and fig. 7 respectively show the difference value sequence of the estimated value of each parameter and the true value of the parameter obtained by the 3 schemes in different situations and the RMSE thereof; fig. 4, 6 and 8 show the coordinate component error and point location error of 3 schemes in different situations, respectively.
It should be noted that the results of scheme 1 were the same in all Cases (3 Cases). For ease of reading and understanding, the results of scheme 1 are not shown in the Case 2 and Case 3 diagrams. Since APs are not considered in case 1, it is not shown in sub-graph g-sub-graph k in fig. 3.
It is necessary here to make a corresponding explanation of the sequence lines in the figure: for fig. 5 and 7, of the 6 left subgraphs, the part near 0 (vertical axis) with less variation is the result of Strategy3 computation, the part with more variation is the result of Strategy 2 computation, and the right subgraph has a similar behavior. However, it should be noted that, in sub-graphs g and h, the variation trends of Strategy 2 and Strategy3 are very similar, which may be caused by the fact that the simulation values of the two constants are much larger than the added random error; for fig. 6 and 8, among the left 4 subgraphs, those closer to 0 (vertical axis) and with more variation trend to the straight line are the results of Strategy3, those farther from 0 and more transformed are the results of Strategy 2, and among the right 4 subgraphs, strategy 2 and Strategy3 have substantially the same variation trend, mainly due to the fact that the check point is not corrected by random errors; for FIG. 3, sub-graph a-sub-graph c, the part near 0 (vertical axis) and with less variation is the computed result of Strategy3, the part near 0 (vertical axis) and with greater variation is the computed result of Strategy 2, the part far from 0 is the computed result of Strategy 1, sub-graph d-sub-graph f, the results of Strategy 2 and Strategy3 are both near 0, but because the trend of the change of the results is not obvious, it is not easy to distinguish in the gray scale map, the right sub-graph has a similar representation, when sub-graph g-sub-graph k does not contain Strategy 1; for FIG. 4, in the left sub-graph 4, the three trend lines are Strategy 1, strategy 2 and Strategy3 from top to bottom, respectively, in the right sub-graph 4, the top trend line is Strategy 1, and the bottom trend lines are the display results of Strategy 2 and Strategy3, and at this time, the variation trend of Strategy 2 and Strategy3 is similar.
From table 1 and fig. 3-8 we can find the following results:
1. scheme 1, without any error correction, the parameter has the greatest deviation from the true value, indicating the necessity for instrument calibration.
2. The results of scheme 2 and scheme 3 are more nearly zero. However, compared to scheme 3, the results of scheme 2 are more scattered, with a larger difference from the true values, and even somewhat exceeding scheme 1 (fig. 3 (c), fig. 5 (c), fig. 7 (c)). It is therefore clear that scheme 3 is more accurate and more stable than scheme 2, especially in terms of translation parameters and shafting errors.
3. Scheme 3 may obtain more accurate APs and EOPs. Considering that the RMSE of the parameters in case 3 is closest to zero after the decimal point is preserved, the accuracy of all parameters is improved relative to case 1 and case 2. For APs, scheme 3 improves by 2%, 48.1%, 30.9%, and 53.7%, respectively, according to the order of the parameter vectors (equations (7), (8)) except for the addition constant m; in 3cases, the accuracy of the EOPs was improved by 48.7% to 84.9% over scheme 2, demonstrating the effectiveness and robustness of the general method.
4. In case 3, the RMSE of the coordinates of the same-name points is much smaller after systematic error correction than in case 2, and increases from 10 "4 to 10" 7, as shown in fig. 3, 5, and 7 (a) to (f), but the remaining points are substantially the same and do not deviate much from each other. On the other hand, if the random error of the observed value is not removed, the RMSE of the same-name point of case 3 has the same tendency as that of case 2.
TABLE 1 RMSE for each parameter vector
Note: "- -" indicates a null value; "C-" represents different situations; "Imp/%" indicates the percent improvement in accuracy of protocol 3 over protocol 2; c '= c/cos θ, i' = i · tan θ.
In addition, a large number of documents and the simulation experiments show that reasonable and correct instrument calibration can effectively weaken the influence of APs on the coordinate sequence and improve the precision of coordinate data.
In many documents, the nominal accuracy is directly used as prior information to participate in the adjustment process, and after-check estimation is omitted, the observed value cannot be matched with proper weight, the resolving accuracy of the APs is weakened, and therefore perfect calibration cannot be achieved. The measured coordinate sequences were used as experimental data, and measured by SOKKIA (NET 1200) total station and Leica (HDS 3000) TLS, and 8 points (5 same-name points were target spheres and 3 check points were planar targets) were measured, as shown in table 2.
TABLE 2.8 original three-dimensional coordinates of points
Based on the above measured data and simulation data calculation results, the following two experimental schemes are designed,
and 5, a general self-checking method of the scanner based on the Gauss-Helmert model and considering random information.
The nominal precision (the measuring range is 4mm, the angle is 0.0033 degrees and the error in unit weight) of the HDS3000 is taken as prior information to be brought into the adjustment process (Case 1), the coordinate observed value of the total station is taken as a true value, and the effectiveness and the practicability of the general self-checking algorithm are analyzed. Further, a case is assumed in which a priori information is unknown and the observed values are handled with equal weight (case 2). HDS300 is implemented using the same 2 schemes described above0 scanner self-calibration, assuming square root of a prior variance component as σ 0 =1, results are shown in table 3,
TABLE 3. Coordinate accuracy of homologous points
As can be seen from table 3, the accuracy of the universal self-calibration model is always the highest in the homonymy part. For both cases (Case 1 and Case 2), the point location accuracy level of the homonymous point can be from 10 respectively -4 Is increased to 10 -8 And 10 -7 . From the results in table 3, it can also be seen that the proposed method not only can detect systematic errors (APs), but also can effectively eliminate the effect of random errors, while being robust to different weighting methods. Since the random error of the check point cannot be estimated, the corrected check point results are similar to the results of the simulation experiment and will not be discussed.
Based on the problem of correlation between EOPs and Aps in the prior art, in the invention, the random error of the observed value is considered to construct a function model and a random model, so that the random error is removed in the processing process, the mutual influence between the random errors is weakened, and the correlation between unknown parameters can be weakened to a certain extent.
Taking the equal weight as an example, fig. 9 shows the distribution of the difference between the absolute values of the correlation coefficients (scheme 4 minus scheme 5) of scheme 4 and scheme 5 under the equal weight condition; wherein 1 to 11 in the horizontal axis and the vertical axis represent Δ x, Δ y, Δ z,
ω, κ, m, λ, c, i, t. Statistical analysis was performed on 110 elements in fig. 8 (without considering diagonal elements), with elements greater than 0 indicating that solution 5 has a lower parameter correlation than solution 4, and vice versa. Of these, 74 elements are larger than 0, and 36 elements are smaller than 0, which shows that the general self-calibration method for scanners based on Gauss-Helmert model and considering random information can weaken the correlation between most parameters (about 67%).
Therefore, compared with other comparative test methods, the test results obtained by the method are closer to the true values, especially in terms of translation parameters and axis errors; and more accurate values of the unknown parameter can be obtained. In addition, random errors are considered in a function model and estimation weights of variance components are adopted, so that the correlation among the parameters can be effectively weakened, and the effectiveness and the robustness of the method are proved.
Example 2
Referring to fig. 8, the present invention provides a system error self-calibration apparatus for a measurement system, configured to obtain a system error value of the measurement system; the device comprises:
the model construction module 10 is configured to construct a first system error self-checking model based on Gauss-Helmert and considering random errors, and determine an unknown parameter vector and a random error vector of the first system error self-checking model; determining a corresponding target function based on the first system error self-checking model; wherein the unknown parameter vector comprises an external conversion parameter and a calibration parameter;
further, the model building module 10 includes: a random error vector submodule 11 and a first system model submodule 12; the random error vector submodule is used for determining a random error vector; and the first system model submodule is used for constructing the first system error self-checking model based on the random error vector, and is a function model of the reference coordinate of the observation point about the original observation coordinate, the rotation parameter, the checking error parameter and the random error vector of the observation point.
A system initial value module 20, configured to obtain an initial value of the unknown parameter vector, an initial value of the random error variable, and an original observed value of a same-name point;
the iterative solution module 30 is configured to perform m (m is greater than or equal to 1) times of iterative solution on the unknown parameter vector and the random error vector on the first system error self-calibration model by using a non-linear least square newton-gaussian method based on the initial value of the unknown parameter vector, the initial value of the random error vector, and the original observed value, so as to obtain a final solution value of the unknown parameter vector that meets a preset convergence condition; the final solution value of the unknown parameter vector comprises a system error value of the measuring system;
further, the iterative solution module 30 includes:
the linear conversion submodule 31 is configured to apply binary taylor series expansion to the first systematic error self-calibration model at the initial iteration value of the unknown parameter vector and the initial iteration value of the random error vector to obtain a second systematic error self-calibration model;
the parameter calculating submodule 32 is configured to construct a lagrangian target function by using the target function and the second system error self-calibration model, and calculate and obtain a calculated value of the unknown parameter vector and the random error vector according to lagrangian requirements;
a parameter determination iteration submodule 33, configured to determine whether a solution value of the unknown parameter vector meets the preset convergence condition, if so, quit the iterative solution process, and use the solution value as a final solution value of the unknown parameter vector to obtain a system error value of the measurement system; otherwise, obtaining a solution value of the unknown parameter vector and a solution value of the random error vector, and respectively replacing the solution values with an initial iteration value of the unknown parameter vector and an initial iteration value of the random error vector.
Wherein the calibration parameter value in the final solution value of the unknown parameter vector is a system error value of the measurement system.
Further, the system error self-calibration device of the measurement system further includes an optimization submodule 34, configured to optimize an iterative solution process of the unknown parameter vector and the random error vector by using a variance component estimation method in a process of executing the iterative solution module program, and obtain a solution value of the unknown parameter that is optimized and satisfies a preset convergence condition.
Specifically, the optimization submodule is configured to execute, and includes:
performing observation value classification on the original observation value;
and adjusting the random error weight matrix according to the observed values in a classified manner to obtain an optimized random error weight matrix, replacing the optimized random error weight matrix with the random error weight matrix in the second system error self-checking model, and executing a program of the iterative calculation module to obtain a calculated value of the unknown parameter vector which satisfies the preset convergence condition after optimization.
It should be noted that the division of each module of the system error self-calibration device of the measurement system is only a division of a logic function, and the actual implementation may be wholly or partially integrated into one physical entity, or may be physically separated. And the modules can be realized in a form that all software is called by the processing element, or in a form that all the modules are realized in a form that all the modules are called by the processing element, or in a form that part of the modules are called by the hardware. For example: the x module can be a separately established processing element, and can also be integrated in a certain chip of the device. The x-module may be stored in the memory of the apparatus as a program code, and may be called by a processing element of the apparatus to execute the following functions of the x-module. Other modules are implemented similarly. All or part of the modules can be integrated together or can be independently realized. The processing element described herein may be an integrated circuit having signal processing capabilities. In implementation, each step of the above method or each following module may be implemented by an integrated logic circuit of hardware in a processor element or an instruction in the form of software. The modules described above may be one or more integrated circuits configured to implement the above methods, such as: one or more Application Specific Integrated Circuits (ASICs), one or more microprocessors (DSPs), one or more Field Programmable Gate Arrays (FPGAs), and the like. When a module is implemented in the form of a Processing element scheduler code, the Processing element may be a general-purpose processor, such as a Central Processing Unit (CPU) or other processor capable of calling program code. These modules may be integrated together and implemented in the form of a System-on-a-chip (SOC).
Example 3
The present invention provides an electronic device, including: a processor, a memory, a transceiver, a communication interface, and a system bus; the memory is used for storing computer programs, the communication interface is used for communicating with other devices, and the processor and the transceiver are used for running the computer programs to enable the processing device to execute the steps of the system error self-checking method of the measuring system.
The Processor may be a general-purpose Processor, including a Central Processing Unit (CPU), a Network Processor (NP), and the like; the Integrated Circuit may also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA) or other Programmable logic device, discrete Gate or transistor logic device, or discrete hardware components.
Example 4
The invention also provides a computer-readable storage medium on which a computer program is stored, which program, when invoked by a processor, implements a method of self-checking system errors of the measurement system. The computer-readable storage medium may include a Random Access Memory (RAM), and may further include a non-volatile memory (non-volatile) such as at least one disk memory.
In summary, the method, the device, the equipment and the computer storage medium for self-checking the system error of the measurement system provided by the invention add the random error information in the constructed system model, and effectively improve the resolving accuracy of the system error parameters in the measurement system by resolving the system model added with the random error information; in addition, the method can also realize a post-test estimation method through variance component estimation under the condition of error of prior information or unknown prior information, and effectively ensures the solving precision of system error parameters.
The foregoing embodiments are merely illustrative of the principles and utilities of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or change the above-mentioned embodiments without departing from the spirit and scope of the present invention. Accordingly, it is intended that all equivalent modifications or changes which may be made by those skilled in the art without departing from the spirit and scope of the present invention as defined in the appended claims.
Claims (9)
1. A system error self-checking method of a measuring system is used for obtaining a system error value of the measuring system, and the method comprises the following steps:
constructing a first system error self-checking model based on Gauss-Helmert and considering random errors, and determining an unknown parameter vector and a random error vector of the first system error self-checking model; determining a target function corresponding to the first system error self-checking model based on the first system error self-checking model; wherein the unknown parameter vector comprises an external conversion parameter and a calibration parameter;
acquiring an initial value of the unknown parameter vector, an initial value of the random error variable and an original observed value of a same-name point;
based on the initial value of the unknown parameter vector, the initial value of the random error vector and the original observed value, performing iterative solution of the unknown parameter vector and the random error vector on the first system error self-checking model by adopting a Newton-Gaussian method of nonlinear least squares to obtain a final solution value of the unknown parameter vector meeting a preset convergence condition; the final solution value of the unknown parameter vector comprises a system error value of the measuring system;
wherein the random error vector of the observation point comprises random errors of a distance, a vertical angle and a horizontal angle;
the first system error self-checking model comprises:
in the formula, X, Y and Z are reference coordinates of the observation points; s, theta and alpha are original observation coordinates of the observation point, and respectively represent the distance from the observation point to the measurement origin, the vertical angle of the observation direction and the horizontal angle of the observation direction; r is a rotation parameter matrix composed of rotation parameters
A matrix of components, wherein,
is the rotation angle of the Y axis, omega is the rotation angle of the X axis, and kappa is the rotation angle of the Z axis; m, lambda, c ', i', t are calibration parameters, wherein m is an addition constant, lambda is a multiplication constant, c 'is an aiming axis related error, i' is a horizontal axis related error, and t is a vertical angle index difference; Δ X, Δ Y, Δ Z represent translation parameters on the X, Y, Z axes, respectively;
the unknown parameter vector is:
in the formula (I), the compound is shown in the specification,
the external conversion parameter is the external conversion parameter; and m, lambda, c ', i' and t are the calibration parameters.
2. The method for self-checking the systematic error of the measurement system according to claim 1, further comprising: and optimizing the iterative solution process by adopting a variance component estimation method in the iterative solution process of the unknown parameter vector and the random error vector of the first system error self-calibration model by adopting a non-linear least square Newton-Gaussian method based on the initial value of the unknown parameter vector, the initial value of the random error vector and the original observed value, so as to obtain the solution value of the unknown parameter which is optimized and meets the preset convergence condition.
3. The method according to claim 1, wherein the iterative solution of the unknown parameter vector and the random error vector is performed on the first system error self-calibration model by a non-linear least squares newton-gaussian method based on an initial value of the unknown parameter vector, an initial value of the random error vector, and the original observed value, and the iterative solution includes:
performing binary Taylor series expansion on the first system error self-checking model at the initial iteration value of the unknown parameter vector and the initial iteration value of the random error vector to obtain a second system error self-checking model;
constructing a Lagrange objective function by using the objective function and the second system error self-checking model, and resolving to obtain resolving values of the unknown parameter vector and the random error vector according to Lagrange requirements;
judging whether the calculation value of the unknown parameter vector meets the preset convergence condition or not, if so, exiting the iterative calculation process, and taking the calculation value as the final calculation value of the unknown parameter vector to obtain a system error value of the measurement system; otherwise, the calculation value of the unknown parameter vector and the calculation value of the random error vector are obtained and are respectively replaced by the iteration initial value of the unknown parameter vector and the iteration initial value of the random error vector, and the iteration calculation is repeatedly executed.
4. The method of self-checking the system error of the measurement system according to claim 1, wherein the obtaining the initial value of the unknown parameter vector comprises:
and solving the initial value of the external conversion parameter in the unknown parameter vector by using a linear Gaussian Markov model, and taking a zero matrix as the initial value of the calibration parameter.
5. The system error self-checking method of the measurement system according to claim 2, wherein the optimizing the iterative solution process by using a variance component estimation method to obtain the optimized solution value of the unknown parameter vector satisfying the predetermined convergence condition comprises:
performing observation value classification on the original observation value; and adjusting the random error weight matrix according to the observed values in a classified manner to obtain an optimized random error weight matrix, replacing the optimized random error weight matrix with the random error weight matrix in the second system error self-checking model, and executing the iterative calculation process to obtain an optimized calculated value of the unknown parameter vector meeting the preset convergence condition.
6. A system error self-calibration apparatus for a measurement system, for obtaining a system error value of the measurement system, the apparatus comprising:
the model construction module is used for constructing a first system error self-checking model based on Gauss-Helmert and considering random errors, and determining an unknown parameter vector and a random error vector of the first system error self-checking model; determining a target function corresponding to the first system error self-checking model based on the first system error self-checking model; wherein the unknown parameter vector comprises an external conversion parameter and a calibration parameter;
the system initial value module is used for acquiring an initial value of the unknown parameter vector, an initial value of the random error variable and an original observed value of the same-name point;
the iterative calculation module is used for performing iterative calculation on the unknown parameter vector and the random error vector on the first system error self-calibration model by adopting a Newton-Gaussian method of nonlinear least square based on the initial value of the unknown parameter vector, the initial value of the random error vector and the original observed value so as to obtain a final calculation value of the unknown parameter vector meeting a preset convergence condition; the final solution value of the unknown parameter vector comprises a system error value of the measuring system;
wherein the random error vector of the observation point comprises random errors of a distance, a vertical angle and a horizontal angle;
the first system error self-checking model comprises:
in the formula, X, Y and Z are reference coordinates of the observation points; s, theta and alpha are original observation coordinates of the observation point, and respectively represent the distance from the observation point to the measurement origin, the vertical angle of the observation direction and the horizontal angle of the observation direction; r is a rotation parameter matrix composed of rotation parameters
A matrix of components, wherein,
is the rotation angle of the Y axis, omega is the rotation angle of the X axis, and kappa is the rotation angle of the Z axis; m, lambda, c ', i', t are calibration parameters, wherein m is an addition constant, lambda is a multiplication constant, c 'is an aiming axis related error, i' is a horizontal axis related error, and t is a vertical angle index difference; Δ X, Δ Y, Δ Z represent translation parameters on the X, Y, Z axes, respectively;
the unknown parameter vector is:
in the formula (I), the compound is shown in the specification,
the external conversion parameter is the external conversion parameter; and m, lambda, c ', i' and t are the calibration parameters.
7. The system error self-calibration device of the measurement system according to claim 6, wherein the iterative solution module comprises:
the linear conversion submodule is used for performing binary Taylor series expansion on the first system error self-checking model at the initial iteration value of the unknown parameter vector and the initial iteration value of the random error vector to obtain a second system error self-checking model;
the parameter calculating submodule is used for constructing a Lagrangian target function by using the target function and the second system error self-checking model, and calculating to obtain a calculated value of the unknown parameter vector and the random error vector according to Lagrangian necessary conditions;
the parameter judgment iteration submodule is used for judging whether the calculation value of the unknown parameter vector meets the preset convergence condition or not, if so, the iteration calculation process is exited, and the calculation value is used as the final calculation value of the unknown parameter vector to obtain a system error value of the measurement system; otherwise, the solution value of the unknown parameter vector and the solution value of the random error vector are obtained and are respectively replaced by the initial iteration value of the unknown parameter vector and the initial iteration value of the random error vector, and the iteration solution module is repeatedly executed.
8. The system error self-calibration device of the measurement system according to claim 6, further comprising:
and the optimization submodule is used for optimizing the iterative calculation process by adopting a variance component estimation method in the process of executing the iterative calculation module program to obtain the optimized calculation value of the unknown parameter meeting the preset convergence condition.
9. The system error self-calibration device of the measurement system according to claim 8, wherein the optimization submodule is configured to perform, and comprises:
carrying out observation value classification on the original observation value;
and adjusting the random error weight matrix according to the observed values in a classified manner to obtain an optimized random error weight matrix, replacing the optimized random error weight matrix with the random error weight matrix in the second system error self-checking model, and executing a program of the iterative calculation module to obtain an optimized calculated value of the unknown parameter vector meeting the preset convergence condition.
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