KR101209571B1 - Autocalibration method and device - Google Patents

Abstract

According to an aspect of the present invention, a method for automatically calibrating a multi-axis sensing device including a plurality of sensors is provided. The method includes acquiring data representing vector physical quantities from a plurality of sensors, performing a predetermined elliptic fitting algorithm on the acquired data to generate an elliptic scale factor value and a calibration bias value, and the generated elliptic scale factor. And generating a calibration scale factor value by performing a predetermined decomposition algorithm on the value.

Description

Automatic calibration method and device {AUTOCALIBRATION METHOD AND DEVICE}

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an automatic calibration technique of a multi-axis sensing device for measuring physical quantities such as acceleration, force, magnetic field, and the like. The present invention relates to a technique for automatically calibrating a multi-axis sensing device.

The physical quantities, such as acceleration, force, and the earth's magnetic field, can be represented by, for example, vector values consisting of X, Y, and Z axis values, which are measured using a multi-axis sensing device consisting of a plurality of sensors. The measured value of the sensing device does not have the same value as the actual physical quantity, and there is a predetermined correspondence between the measured value and the actual physical quantity. This correspondence is generally represented by a scale factor value E and a bias value B. That is, when the measured value is Z and the actual physical quantity is X, it has a relationship of Z = E * X + B. However, since the corresponding relationship between the measured value and the actual physical quantity is generally different from each sensing device, in order to accurately measure the actual physical quantity using the sensing device, the corresponding relationship between the measured value of the corresponding sensing device and the actual physical quantity Must be performed beforehand.

In the related art, a calibration method of determining a scale factor value and a bias value from the above-described physical quantities and the measured values of the sensing apparatuses, after confirming in advance what kind of physical quantity to input to the sensing apparatus, has been used. However, this method requires not only an additional sensor for identifying physical quantities in advance, but also requires a long time and cost for calibration. Accordingly, in recent years, research has been made on a technique for automatically calibrating a multi-axis sensing apparatus without the aid of an additional sensor. However, a robust automatic calibration technique, such as noise and disturbance, has not yet been provided.

The present invention relates to a calibration technique of a sensing device that measures a vector physical quantity such as acceleration, force, earth magnetic field, etc., and a method in which the sensing device is automatically calibrated without the aid of an additional sensor and even if the sensing device is moved in any direction. And an apparatus for that purpose.

Another object of the present invention is to provide a method and apparatus for automatically calibrating a sensing device using a condition that a magnitude of a physical quantity vector corresponding to an input of the sensing device is constant.

Another object of the present invention is to provide a method and apparatus for automatically calibrating a sensing device that is robust against disturbances, noise, and the like without utilizing local minimum and maximum information of measured values.

According to an aspect of the present invention, a method for automatically calibrating a multi-axis sensing device including a plurality of sensors is provided. The method includes acquiring data representing vector physical quantities from a plurality of sensors, performing a predetermined elliptic fitting algorithm on the acquired data to generate an elliptic scale factor value and a calibration bias value, and the generated elliptic scale factor. And generating a calibration scale factor value by performing a predetermined decomposition algorithm on the value.

According to another aspect of the present invention, an apparatus for automatically calibrating a multi-axis sensing device comprising a plurality of sensors is provided. The apparatus obtains data representing a vector physical quantity from a plurality of sensors, and performs an elliptic fitting algorithm on the obtained data to generate an elliptic scale factor value and a calibration bias value, and an elliptic scale generated. And a decomposition unit configured to generate a calibration scale factor value by performing a predetermined decomposition algorithm on the factor values.

According to the present invention as described above, it is possible to provide a method and apparatus capable of automatically calibrating a sensor for measuring a vector physical quantity without having to install an additional sensor in the sensing device and moving the sensing device in any direction. In addition, the present invention can provide a method and apparatus capable of robustly calibrating a sensing device even in the presence of noise and disturbance.

1 is a conceptual diagram of a multi-axis sensing device according to an embodiment of the present invention.
2 is a conceptual diagram illustrating a correspondence relationship between a measured value vector and an actual physical quantity vector of a multi-axis sensing device according to an exemplary embodiment of the present invention.
3 is a block diagram of a multi-axis sensing device according to an embodiment of the present invention.
4 is a flowchart illustrating an automatic calibration method of a multi-axis sensing device according to an exemplary embodiment of the present invention.
5 is a view showing the experimental results of the automatic calibration method according to an embodiment of the present invention.
6 is a view showing the results of experiments performed in the acceleration sensing device implemented according to an embodiment of the present invention.
7 is a view showing the results of experiments performed on the calibration of the electronic compass implemented in accordance with one embodiment of the present invention.

Reference is now made to the accompanying drawings, which form a part of this specification. In the drawings, like numerals refer to similar constructions unless the context clearly indicates otherwise. The illustrative embodiments described in the detailed description, drawings, and claims are not meant to be limiting. Other embodiments may be implemented and other changes may be made without departing from the spirit or scope of the subject matter presented herein. It will be readily understood that the components of the present disclosure generally described herein and illustrated in the drawings can be arranged, replaced, or combined in various other configurations, all of which constitute part of this specification. do.

1 is a conceptual diagram of a multi-axis sensing device according to an embodiment of the present invention. Referring to FIG. 1, the multi-axis sensing device 100 is an apparatus for measuring a vector physical quantity composed of a plurality of axis values (for example, X, Y, and Z axis values), and includes a plurality of sensors (for example, a first sensor). To third axis sensors 101-103. The plurality of sensors may be sensors that measure one or more predetermined physical quantities such as acceleration, force, and earth magnetic field. The specific configuration of the multi-axis sensing device 100 is well known in the art, and will not be described in detail below.

Hereinafter, the concept of the calibration applied to the multi-axis sensing device 100 according to an embodiment of the present invention will be described in detail. The measured value of the multi-axis sensing device 100 does not have the same value as the measured actual physical quantity, and there is a predetermined correspondence between the measured value and the actual physical quantity. This correspondence can be represented by the following equation.

Where Z is the measurement vector, X is the actual physical quantity vector, E is the calibration scale factor matrix, and b is the calibration bias vector. In the present invention, the term “correction” refers to a task of obtaining a corresponding relationship between the measured value vector and the actual physical quantity vector of the multi-axis sensing apparatus 100, that is, the task of obtaining E and b.

)인 단위 구로 가정할 경우, 타원체(202)는 아래 수식으로 나타낼 수 있다.In one embodiment, the multi-axis sensing device 100 of the present invention may perform calibration on the assumption that the magnitude of the actual physical quantity vector to be measured is constant. 2 is a conceptual diagram illustrating a correspondence relationship between a measured value vector and an actual physical quantity vector of a multi-axis sensing device according to an exemplary embodiment of the present invention. Referring to FIG. 2, FIG. 2A shows a sphere 201 which is a set of actual physical quantity vectors having a constant size. When the multi-axis sensing device 100 measures the physical quantity vectors having such a constant size, the measured value vectors obtained form the ellipsoid 202 as shown in FIG. Sphere 201 has a norm of 1 (

Assuming that the unit sphere is), the ellipsoid 202 can be represented by the following formula.

Where Z is the measurement vector, X is the actual physical quantity vector, M ^-1 is the first elliptic scale factor matrix between the sphere 201 and the ellipsoid 202, and b is the center value of the sphere 201 and the ellipsoid 202. Represents the distance vector between the central values of.

로 분해(decomposition)될 수 있는 행렬인 경우,

로 나타낼 수 있다. 여기서, U는 각 열이 E의 고유 값(eigenvalue)인 고유 벡터(eigenvector)이고

는 E의 고유값의 대각 행렬 (diagonal matrix)이다. The distance vector b between the center value of the sphere 201 and the center value of the ellipsoid 202 of the above equation is equal to the calibration bias vector b. And, the elliptic scale factor matrix M ^-1 between the sphere 201 and the ellipsoid 202 is a correction factor matrix E is

If the matrix can be decomposed into

. Where U is an eigenvector where each column is an eigenvalue of E

Is a diagonal matrix of eigenvalues of E.

를 구하고, 이들로부터

인 교정 스케일 인자 행렬 E를 구한다.One embodiment of the present invention focuses on the above, (1) performing a predetermined elliptic fitting algorithm on the measurement vector obtained from the multi-axis sensing apparatus 100 to calibrate with the elliptic scale factor matrix M ^{- 1} U which constructs M by obtaining a bias value b and (2) performing a predetermined decomposition algorithm on the elliptic scale factor matrix M ^-1 .

To obtain

Find the calibration scale factor matrix E

Hereinafter, a detailed configuration of the multi-axis sensing device and its operation method according to an embodiment of the present invention will be described in detail. 3 is a block diagram of a multi-axis sensing device according to an embodiment of the present invention. Referring to FIG. 3, the multi-axis sensing device 300 may include a sensor unit 310, an elliptic alignment unit 320, and a decomposition unit 330.

The sensor unit 310 may include a plurality of sensors. In one embodiment, at least one of the plurality of sensors may be a linear sensor. In another embodiment, at least one of the plurality of sensors may be a nonlinear sensor. In one embodiment, the plurality of sensors may be sensors configured to measure a physical quantity of any one of acceleration, force, and earth magnetic field.

The elliptic fitting unit 320 may be configured to obtain data representing a vector physical quantity from a plurality of sensors, and to perform an elliptic alignment algorithm on the acquired data to generate an elliptic scale factor value and a calibration bias value. In one embodiment, the elliptic fitting algorithm may be a semi-definite programming (SDP) algorithm. For information about the SDP algorithm, see Giuseppe Calafiore, "Approximation of n-Dimensional Data Using Spherical and Ellipsoidal Primitives," IEEE Trans. Syst., Man., Cybern. A, vol 32, no. 2, pp. 269-278, 2002.

The decomposition unit 330 may be configured to generate a calibration scale factor value by performing a predetermined decomposition algorithm on the generated elliptic scale factor value. In one embodiment, the decomposition algorithm may be a singular value decomposition (SVD) algorithm. SVD algorithms are well known in the art and will not be described in detail.

4 is a flowchart illustrating an automatic calibration method of a multi-axis sensing apparatus according to an embodiment of the present invention. Referring to FIG. 4, the method obtains data representing vector physical quantities from a plurality of sensors of the multi-axis sensing apparatus (step 410), and performs an elliptic fitting algorithm on the acquired data to obtain an elliptic scale factor value and a calibration bias value. In step 420, a calibration factor is generated by performing a predetermined decomposition algorithm on the generated elliptic scale factor value (step 430), and the procedure ends. In one embodiment, the elliptic fit algorithm may be an SDP algorithm, and the algorithm may be an SVD algorithm.

Hereinafter, specific details of the operation operations performed in each step illustrated in FIG. 4 will be described in detail using equations.

Definition and notation

Hereinafter, a plurality of sensors of the multi-axis sensing device measure physical quantities (acceleration, force, earth magnetic field, etc.) and assume that they are not calibrated. The measured value, which is the data generated by the sensor measuring the physical quantity X = [x ₁ , x ₂ , x ₃ ] ^T , can be expressed as a vector Z. The relation for calibration of multi-axis sensing device is as follows.

here,

In the above equation, the unknown values are the physical quantity X, the calibration bias vector b, and the calibration scale factor matrix E to be measured. The only known value in the above equation is the vector Z, which corresponds to the sensor's measurement data. To calibrate the multi-axis sensing device is to calculate the calibration bias vector b and the calibration scale factor matrix E.

Although the magnitude and direction of the vector physical quantity X are not known, it may be assumed that the sensing device measures and corrects the vector physical quantity X under constant conditions. In order to maintain a constant magnitude of the vector physical quantity to be measured, when the sensing device is an acceleration sensing device, gravity acceleration may be measured in a state in which there is little movement. In the case where the sensing device is an electronic compass, the surrounding magnetic field may be used. It is possible to measure the magnetic field in this relatively small environment. In the case of the force sensing device, a predetermined object may be used so that the magnitude of the force applied to the force sensor is constant. The calibration scale factor matrix can be assumed to be a symmetric positive definite matrix with a symmetrical form.

1. Acquiring data representing the vector physical quantity

The multi-axis sensing apparatus may measure data corresponding to the vector physical quantity X whose direction is not known, and may acquire a plurality of data Z by performing the measurement while varying the direction of the multi-axis sensing apparatus to vary the direction of X. In the case of an electronic compass, X corresponds to the Earth's magnetic field vector, and varying the direction of X involves rotating the electronic compass in any direction.

2. On acquired data SDP  Performing an algorithm to generate elliptic scale factor values and calibration bias values

로 표현할 수 있다. 여기서, U는 각 열이 E의 고유 값인 고유 벡터이고

는 E의 고유 값의 대각 행렬이다. The correction scale factor matrix E is assumed to be a symmetric positive definite matrix with symmetrical form.

. Where U is an eigenvector where each column is a unique value of E

Is a diagonal matrix of eigenvalues of E.

When the sensor measures the j-th measured data using a superscript, Equation 1 may be expressed as Equation 4 below.

The magnitude (norm) of the left and right side vectors of Equation 4 may be normalized to one.

 Equation 6 below is calculated from Equation 5

By applying the SDP algorithm to the obtained measurement vector Z, an elliptic scale factor matrix M and a calibration bias vector b can be obtained. Hereinafter, the SDP algorithm will be described.

에 대한 거리 메트릭은 다음과 같이 정의될 수 있다.procession

The distance metric for may be defined as follows.

은 다음과 같이 정의될 수 있다.Optimization Criteria for the SDP Algorithm Using the Above Distance Metric

May be defined as follows.

,

,

이다. here,

,

,

to be.

가

(j=1,…,N)를 그 구성요소가 양의 스칼라 값인 벡터이고,

가 1로 이루어진 벡터(즉,

)인 경우에,

,

,

및

를 변수로 하는 SDP 알고리즘은 다음 수식을 제한 조건으로 하여

를 최소화하는 알고리즘이다.

end

(j = 1,…, N) is a vector whose components are positive scalar values,

Is a vector of 1s (i.e.

)in case of,

,

,

And

The SDP algorithm using as a variable

Is an algorithm that minimizes

,

,

및

로 표현시, 다음 값들을 갖는 타원체는 DOS(difference of sum) 기준을 글로벌 최소화하는 타원체(global minimizer)이다.Symbol of the optimal value that can be obtained

,

,

And

The ellipsoid having the following values is an ellipsoid that globally minimizes the difference of sum (DOS) criterion.

For more information on the SDP algorithm, see Giuseppe Calafiore, "Approximation of n-Dimensional Data Using Spherical and Ellipsoidal Primitives," IEEE Trans. Syst., Man., Cybern. A, vol 32, no. 2, pp. 269-278, 2002, the following further description is omitted.

3. Generating a calibration scale factor value by performing a predetermined decomposition algorithm on the generated elliptic scale factor value

을 수학식 6에 대입하면 U와

행렬을 얻을 수 있다. 따라서 구하고자 하는 교정 스캐일 인자 행렬 E는

로부터 계산된다. 결과적으로, 교정에 필요한 교정 바이어스 벡터 b와 교정 스케일 팩터 행렬 E를 모두 계산할 수 있다.Elliptic Scale Factor Matrix

Is substituted into Equation 6, U and

You can get a matrix. Therefore, the calibration scale factor matrix E

Is calculated from As a result, both the calibration bias vector b and the calibration scale factor matrix E required for the calibration can be calculated.

The method described above can be implemented using the following exemplary MATLAB algorithm.

% [Step 1]

raw_data = load ('sensor.txt');

[n, n0] = size (raw_data)

z = raw_data;

u = ones (n, 1);

cvx_begin sdp

variable gamma (n);

variables f (3) d (1);

variable P (3,3) symmetric;

expressions Omega (4,4);

minimize (trace (gamma * U '));

subject to

Omega = [P f; ...

f 'd];

for k = 1: n

gamma (k)> 0;

g_omega = quad_form ([z (k, 1); z (k, 2); z (k, 3); 1], Omega);

gamma (k)-g_omega> 0

gamma (k) + g_omega> 0;

end

trace (P) == 1;

P> 0;

cvx_end

disp (P)

b = (-1) * inv (P) * f

sqr_radius = abs (b '* P * b -d)

inv_P = inv (P);

M = inv_P. * Sqr_radius

% [Step 2]

[u D2 V] = svd (M)

D = D2 ^ (1/2)

E = U * D * V '

Inv_E = inv (E)

5 is a view showing the experimental results of the automatic calibration method according to an embodiment of the present invention. As shown in FIG. 5, the calibration is robustly performed even when there are a large number of noises, disturbances, and outliers in the measured values. FIG. 6 is a diagram illustrating an experimental result of performing calibration in an acceleration sensing device implemented according to an embodiment of the present invention. FIG. FIG. 7 is a diagram illustrating an experiment result of performing calibration on an electronic compass implemented according to an embodiment of the present invention. FIG. As shown in Figures 6 and 7, the present invention is not limited to the electronic compass has the advantage that it can be applied to any sensor for measuring any physical quantity such as acceleration, force, earth magnetic field. For example, according to the exemplary embodiment, the calibration may be performed in the same manner without distinction between the electronic compass device and the acceleration measurement device. In addition, according to the exemplary embodiment of the present invention described above, even when the axis sensors of the multi-axis sensing apparatus are disposed to be twisted with each other without being orthogonal to each other, robust calibration can be performed.

Those skilled in the art will appreciate that the functions, processes, operations, interactions, and methods described herein may be implemented in a different order and / or manner than the illustrated order and / or manner. In addition, the described steps and acts are illustrative ones, some of which may be optional and may be combined into fewer steps and acts or extended to further steps and acts without departing from the nature of the disclosed embodiments. Can be.

Those skilled in the art will also appreciate that the devices and methods described herein may be implemented in hardware, software, firmware, middleware, or combinations thereof, and may be used in systems, subsystems, components, or subcomponents thereof. Will know. For example, a method implemented in software can include computer code for performing the operations of the method. Such computer code may be stored on a machine readable medium, such as a processor readable medium or a computer program product, or transmitted over a transmission medium or communication link as a computer data signal embodied as a carrier wave or a signal modulated by a carrier wave. . Machine-readable media or processor-readable media can include any medium that can store or convey information in a form that can be read and executed by a machine (eg, processor, computer, etc.).

From the foregoing, various embodiments of the present disclosure have been described for purposes of illustration, and may be embodied in various modified forms without departing from the scope and spirit of the present disclosure. Accordingly, the various embodiments described herein are not to be taken in a limiting sense, and the true scope and spirit of the specification are indicated by the following claims.

Claims (6)

An automatic calibration method of a multi-axis sensing device including a plurality of sensors,
Acquiring data representing vector physical quantities from the plurality of sensors;
Generating an elliptic scale factor value and a calibration bias value by performing a predetermined elliptic fitting algorithm on the obtained data;
Generating a calibration scale factor value by performing a predetermined decomposition algorithm on the generated elliptic scale factor value
Including, automatic calibration method. The method of claim 1,
Generating the elliptic scale factor value and the calibration bias value,
And performing a semi-definite programming (SDP) algorithm on the obtained data. The method of claim 1,
Generating the calibration scale factor value,
Generating a calibration scale factor value by performing a singular value decomposition (SVD) algorithm on the generated elliptic scale factor value
Including, automatic calibration method. An apparatus for automatically calibrating a multi-axis sensing device including a plurality of sensors,
An elliptic fitting unit configured to acquire data representing a vector physical quantity from the plurality of sensors and to perform an elliptic fitting algorithm predetermined on the obtained data to generate an elliptic scale factor value and a calibration bias value; And
A decomposition unit configured to generate a calibration scale factor value by performing a predetermined decomposition algorithm on the generated elliptic scale factor value
Including, automatic calibration device. The method of claim 4, wherein the elliptic fitting portion,
And perform an SDP algorithm on the obtained data to generate the elliptic scale factor value and the calibration bias value. The method of claim 4, wherein the decomposition unit,
And perform an SVD algorithm on the generated elliptic scale factor value to generate the calibration scale factor value.

Images