CN110647282A - Handwritten track information acquisition method - Google Patents

Handwritten track information acquisition method Download PDF

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Publication number
CN110647282A
CN110647282A CN201910883816.6A CN201910883816A CN110647282A CN 110647282 A CN110647282 A CN 110647282A CN 201910883816 A CN201910883816 A CN 201910883816A CN 110647282 A CN110647282 A CN 110647282A
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electronic pen
matrix
information
angle
accelerometer
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崔敏
周昕雨
黄用
孟铭
王鹏程
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North University of China
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North University of China
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F3/00—Input arrangements for transferring data to be processed into a form capable of being handled by the computer; Output arrangements for transferring data from processing unit to output unit, e.g. interface arrangements
    • G06F3/01—Input arrangements or combined input and output arrangements for interaction between user and computer
    • G06F3/048—Interaction techniques based on graphical user interfaces [GUI]
    • G06F3/0487—Interaction techniques based on graphical user interfaces [GUI] using specific features provided by the input device, e.g. functions controlled by the rotation of a mouse with dual sensing arrangements, or of the nature of the input device, e.g. tap gestures based on pressure sensed by a digitiser
    • G06F3/0488—Interaction techniques based on graphical user interfaces [GUI] using specific features provided by the input device, e.g. functions controlled by the rotation of a mouse with dual sensing arrangements, or of the nature of the input device, e.g. tap gestures based on pressure sensed by a digitiser using a touch-screen or digitiser, e.g. input of commands through traced gestures
    • G06F3/04883—Interaction techniques based on graphical user interfaces [GUI] using specific features provided by the input device, e.g. functions controlled by the rotation of a mouse with dual sensing arrangements, or of the nature of the input device, e.g. tap gestures based on pressure sensed by a digitiser using a touch-screen or digitiser, e.g. input of commands through traced gestures for inputting data by handwriting, e.g. gesture or text
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F3/00—Input arrangements for transferring data to be processed into a form capable of being handled by the computer; Output arrangements for transferring data from processing unit to output unit, e.g. interface arrangements
    • G06F3/01—Input arrangements or combined input and output arrangements for interaction between user and computer
    • G06F3/03—Arrangements for converting the position or the displacement of a member into a coded form
    • G06F3/033—Pointing devices displaced or positioned by the user, e.g. mice, trackballs, pens or joysticks; Accessories therefor
    • G06F3/0346—Pointing devices displaced or positioned by the user, e.g. mice, trackballs, pens or joysticks; Accessories therefor with detection of the device orientation or free movement in a 3D space, e.g. 3D mice, 6-DOF [six degrees of freedom] pointers using gyroscopes, accelerometers or tilt-sensors
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F3/00—Input arrangements for transferring data to be processed into a form capable of being handled by the computer; Output arrangements for transferring data from processing unit to output unit, e.g. interface arrangements
    • G06F3/01—Input arrangements or combined input and output arrangements for interaction between user and computer
    • G06F3/03—Arrangements for converting the position or the displacement of a member into a coded form
    • G06F3/033—Pointing devices displaced or positioned by the user, e.g. mice, trackballs, pens or joysticks; Accessories therefor
    • G06F3/0354—Pointing devices displaced or positioned by the user, e.g. mice, trackballs, pens or joysticks; Accessories therefor with detection of 2D relative movements between the device, or an operating part thereof, and a plane or surface, e.g. 2D mice, trackballs, pens or pucks
    • G06F3/03545—Pens or stylus

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  • Theoretical Computer Science (AREA)
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Abstract

The invention discloses a handwritten track information acquisition method, which provides linear acceleration and angular velocity information of a penholder along a roll axis, a pitch axis and a course axis to an electronic pen processor through a handwriting perception system, the processor can calculate a first-order differential matrix of a carrier coordinate system and a direction cosine matrix of a geographic coordinate system in real time according to a direction cosine matrix differential equation, calculates a direction cosine matrix which is converted between the two coordinate systems by taking inertia information of inertial navigation before starting a pen as an initial condition, and can acquire attitude information of a carrier in real time through calculation of the matrix. The invention breaks away from the constraint of a handwriting board, can write in any place such as air, a desktop, paper and the like, and can play a great role in promoting the handwriting input technology.

Description

Handwritten track information acquisition method
Technical Field
The invention belongs to the technical field of information perception and man-machine interaction, and particularly relates to a handwritten track information acquisition method.
Background
With the development of computer science and technology, man-machine interaction modes gradually develop from keyboard and mouse interaction modes to pen type, voice and vision natural interaction modes. Among these, pen interaction is the most desirable interaction, both in terms of convenience, naturalness and controllability. Based on these advantages of pen-based interaction, in recent years, various handwriting input devices are in a great variety, which can more accurately capture a handwriting track of a user, and provide a wider development prospect for realizing handwriting input in a computer. The handwriting input of the computer is completed by the handwriting input equipment, which is a basic function of pen type interaction. The pen-type interaction technology is an important interaction mode in the man-machine interaction technology, particularly the multi-channel interaction technology, and efficient interaction can be realized by a user at the fastest speed by providing interaction modes such as sketching, writing gestures and the like. Handwriting is an important way for information interaction between people. With the development of the internet, handwriting can also be used as an important interactive tool between people and between human and machine. From the development process of the computer, the traditional desktop computer is gradually replaced by the mobile computer, and now the development is more towards the tablet computer, which also means the significant change of the man-machine interaction mode, and the man-machine interaction technology of the natural computing mode including pen type, vision and voice is more widely applied.
The common handwriting products on the market at present are composed of a pen and a substrate, the interaction between the pen and the substrate can achieve the functions of writing and drawing, and the digital handwriting board is divided into the following types according to the working principle: resistive pressure plates, electromagnetic induction plates, and capacitive touch pads. The existing mode does not deviate from the constraint of a handwriting board, and restricts the handwriting input technology.
Disclosure of Invention
In order to overcome the constraint of a handwriting board in the prior art, the invention provides the method for acquiring the handwriting track information, which is free from the constraint of the handwriting board, can write in any places such as air, a desktop, paper and the like and can greatly promote the handwriting input technology.
The technical scheme adopted by the invention for realizing the purpose is as follows:
a handwritten track information acquisition method comprises the following steps: the position after the electronic pen switch is turned on is recorded as the initial position S0(ii) a From a starting position S0The inertial information is used as an initial condition, along with the spatial movement of the electronic pen, twelve MEMS accelerometers in the electronic pen can calculate the linear acceleration and the angular velocity information of the roll, pitch and course axes of the electronic pen according to an attitude calculation algorithm embedded in an FPGA in advance through a handwriting sensing system, and after the electronic pen processor obtains the linear acceleration and the angular velocity information, the direction cosine matrix differential equation obtained at the moment is as follows:
Figure BDA0002205203710000011
Figure BDA0002205203710000012
for three-axis angular velocity omegax、ωy、ωzThe formed anti-symmetric matrix is a matrix with a plurality of anti-symmetric matrixes,
Figure BDA0002205203710000013
a direction cosine matrix for the solution; solving a direction cosine matrix differential equation in real time according to a first-order differential matrix of a direction cosine matrix of an electronic pen carrier coordinate system and a geographic coordinate system to obtain a direction cosine matrix representing the posture of the electronic pen, and then integrating linear acceleration information and updating an equation of the speed of the electronic pen; further integrating the linear acceleration information to deduce the track change displacement of the electronic pen; after the angular acceleration of the roll, the pitch and the course axis is subjected to secondary integration, the angle change of the electronic pen is obtained, so that the track change of the electronic pen is calculated, the attitude parameter information of the electronic pen is obtained in real time, and the track change of the electronic pen is displayed on a two-dimensional screen.
Further, the speed update equation of the electronic pen is a direction cosine matrix update equation, and the direction cosine matrix update equation is as follows:
Figure BDA0002205203710000021
Figure BDA0002205203710000022
whereinIs [ t ]m-1,tm]Angular increment within a time period and noting the value of delta thetam＝|Δθm|。
Furthermore, the calculation of the linear acceleration and the angular velocity information of the roll, pitch and course axes of the electronic pen adopts a twelve-degree-of-freedom configuration scheme diagram, the arrow direction corresponding to each number is the measuring direction of the accelerometer, the O point corresponds to the mass center of the pen, the accelerometer cannot be installed at the mass center, the Z axis is the axial direction of the pen, and the change of the track posture of the pen holder is measured by using the cantilever effect of the accelerometer;
the sensitive direction of each accelerometer is respectively set as
Figure BDA0002205203710000024
And the installation position of each accelerometer is as follows:
Figure BDA0002205203710000025
the specific force equation for twelve accelerometers is:
Figure BDA0002205203710000026
f2＝aωzωx-aαy+Az
Figure BDA0002205203710000027
f4＝-aωzωx+aαy+Az
Figure BDA0002205203710000031
f6＝aωzωy-aax+Az
Figure BDA0002205203710000032
f8＝-aωzωy+aαx+Az
Figure BDA0002205203710000033
Figure BDA0002205203710000034
Figure BDA0002205203710000036
in the formula: omegax、ωyAnd ωzAre the angular velocity components of the electronic pen, respectively; alpha is alphax、αyAnd alphazRespectively the angular acceleration component of the electronic pen; a. thex、AyAnd AzAcceleration components at the centroid of the electronic pen, respectively;
and the analytic solutions of the three axial angular velocities of the electronic pen satisfy the following relations:
Figure BDA0002205203710000037
Figure BDA0002205203710000038
Figure BDA0002205203710000039
in the formula:
Figure BDA00022052037100000310
Figure BDA0002205203710000041
Figure BDA0002205203710000042
Figure BDA0002205203710000043
because the installation error angle is very small, the following 3 small rotations are used for sequentially describing:
Figure BDA0002205203710000045
in the formula:
Figure BDA0002205203710000046
the mounting error angle of each accelerometer can be measured by a multi-position test through a discrete calibration method;
the specific force equation for the twelve accelerometer outputs containing the error is thus expressed as:
Figure BDA0002205203710000047
in actual test, the value on the left side of the above formula is measured by the test system in real time, and the value at any moment is recorded as
Figure BDA0002205203710000048
Namely the above type is changed into
Figure BDA0002205203710000049
This is a mathematical model of the calculated angular velocity including the mounting error, and the instantaneous angular velocity at that time can be obtained from each instantaneous system of solved equations.
Preferably, each accelerometer in the twelve degree-of-freedom configuration map is equidistant or close to the centroid point.
Further, an ICA blind source separation method is adopted for acquiring the attitude parameter information of the electronic pen, and the ICA blind source separation method includes the following steps: firstly, measuring Gaussian characteristics of electronic pen aliasing signals acquired from an electronic pen through fourth-order cumulant, and dividing random variables into a super-Gaussian random variable, namely, a kurtosis is positive, a Gaussian random variable, namely, the kurtosis is zero, and a sub-Gaussian random variable, namely, the kurtosis is negative according to the positive and negative of a kurtosis value, wherein the super-Gaussian signal has a typical 'long-tip' probability density function curve, and the typical super-Gaussian distribution is Laplace distribution; secondly, performing Wavelet decomposition by using Wavelet and combining Principal Component Analysis (PCA), and calculating the number of signal sources; and finally, separating noise signals such as motion signals of the electronic pen, installation error noise and the like through Independent Component Analysis (ICA) to obtain attitude parameter information of the electronic pen.
Further, the calculation of the direction cosine matrix of the mutual conversion between the two coordinate systems is to measure the specific force of the electronic pen in each axial direction of the carrier coordinate system by using the accelerometer, and the navigation calculation can be performed only by converting the output information of the accelerometer into the navigation coordinate system, wherein the matrix required by the conversion is the attitude matrixI.e. a transformation matrix between the carrier coordinate system and the navigation coordinate system,
Figure BDA0002205203710000052
the relative position between the two coordinate systems can be determined with three independent rotation angles, which can be represented by three coordinate rotations in the following order: the first rotation is xnynznAround znPositive rotation of the shaft
Figure BDA0002205203710000053
Angle of arrival xn1yn1zn1A location; the second rotation is xn1yn1zn1Around xn1The shaft being rotated forwardly through an angle theta to xn2yn2zn2A location; the third rotation is xn2yn2zn2Around yn2Is rotated through an angle gamma to xbybzbA location;
Figure BDA0002205203710000054
wherein
Figure BDA0002205203710000055
Theta and gamma are respectively expressed as a heading angle, a pitch angle and a roll angle of the carrier. According to the rotation sequence, a coordinate conversion relation from a navigation coordinate system to a carrier coordinate system can be obtained;
attitude transformation matrix
Figure BDA0002205203710000056
Is the angle of course
Figure BDA0002205203710000057
Gamma functions of pitch angle theta and roll angle, of
Figure BDA0002205203710000058
Can determine
Figure BDA0002205203710000059
θ、γ；
Assume that the directional cosine matrix is represented as:
the attitude angle is then:
θ＝sin-1(T32)
Figure BDA00022052037100000512
preferably, the electronic pen comprises an electronic pen main body, a laser light source is arranged at the bottom of the electronic pen main body, a handwriting switch is arranged at the top of the electronic pen main body, the laser switch is arranged on the side face of the electronic pen main body, an electronic pen processor and a handwriting sensing system are arranged in the electronic pen main body, and the handwriting switch, the laser light source, the laser switch and the handwriting sensing system are respectively connected with the electronic pen processor.
The invention provides the linear acceleration and the angular speed information of the penholder along the rolling, pitching and course axes to the electronic pen processor through the handwriting perception system, the processor can calculate the first order differential matrix of the carrier coordinate system and the direction cosine matrix of the geographic coordinate system in real time according to the direction cosine matrix differential equation, the direction cosine matrix which is converted between the two coordinate systems is calculated by taking the inertia information of inertial navigation before starting pen as the initial condition, and the attitude information of the carrier can be obtained in real time through the calculation of the matrix. The invention breaks away from the constraint of a handwriting board, can write in any place such as air, a desktop, paper and the like, and can play a great role in promoting the handwriting input technology.
Drawings
The invention is further described with reference to the accompanying drawings, in which:
FIG. 1 is a twelve degree-of-freedom configuration model;
FIG. 2 is a flow chart of accelerometer signal processing;
FIG. 3 is a flow chart of blind source separation;
FIG. 4 is a flow chart of a carrier attitude calculation and error correction method;
FIG. 5 is a diagram of a transformation relationship between a navigation coordinate system and a carrier coordinate system;
fig. 6 is a front view of the electronic pen.
1. Laser lamp source, 2, laser switch, 3, handwriting switch.
Detailed Description
As shown in fig. 1, the method for acquiring handwritten track information of this embodiment includes the following steps: the position after the electronic pen switch is turned on is recorded as the initial position S0(ii) a From a starting position S0The inertial information is used as an initial condition, along with the spatial movement of the electronic pen, twelve MEMS accelerometers in the electronic pen can calculate the linear acceleration and the angular velocity information of the roll, pitch and course axes of the electronic pen according to an attitude calculation algorithm embedded in an FPGA in advance through a handwriting sensing system, and after the electronic pen processor obtains the linear acceleration and the angular velocity information, the direction cosine matrix differential equation obtained at the moment is as follows:
Figure BDA0002205203710000061
Figure BDA0002205203710000062
for three-axis angular velocity omegax、ωy、ωzA component antisymmetric matrix.
Figure BDA0002205203710000063
A direction cosine matrix for the solution; according to a carrier coordinate system of the electronic pen and a first-order differential matrix of a direction cosine matrix of a geographic coordinate system, solving a direction cosine matrix differential equation in real time to obtain a direction cosine matrix representing the posture of the electronic pen, integrating linear acceleration information, updating a speed equation of the electronic pen, integrating the speed, and deducing the track change displacement of the electronic pen; obtaining the angle of the electronic pen after carrying out secondary integration on the angular acceleration of the roll, the pitch and the course axisAnd the degree is changed, so that the track change of the electronic pen is calculated, the attitude parameter information of the electronic pen is acquired in real time, and the track change of the electronic pen is displayed on a two-dimensional screen.
Further, the speed update equation of the electronic pen is a direction cosine matrix update equation, and the direction cosine matrix update equation is as follows:
Figure BDA0002205203710000072
wherein
Figure BDA0002205203710000073
Is [ t ]m-1，tm]Angular increment within a time period and noting the value of delta thetam＝|Δθm|。
Furthermore, the calculation of the linear acceleration and the angular velocity information of the roll, pitch and course axes of the electronic pen adopts a twelve-degree-of-freedom configuration scheme diagram, the arrow direction corresponding to each number is the measuring direction of the accelerometer, the O point corresponds to the mass center of the pen, the accelerometer cannot be installed at the mass center, the Z axis is the axial direction of the pen, and the change of the track posture of the pen holder is measured by using the cantilever effect of the accelerometer;
the sensitive direction of each accelerometer is respectively set as
Figure BDA0002205203710000074
And the installation position of each accelerometer is as follows:
Figure BDA0002205203710000075
the specific force equation for twelve accelerometers is:
Figure BDA0002205203710000076
f2＝aωzωx-aαy+Az
Figure BDA0002205203710000077
f4＝-aωzωx+aαy+Az
Figure BDA0002205203710000078
f6＝aωzωy-aαx+Az
f8＝-aωzωy+aαx+Az
Figure BDA0002205203710000082
Figure BDA0002205203710000083
Figure BDA0002205203710000084
Figure BDA0002205203710000085
in the formula: omegax、ωyAnd ωzAre the angular velocity components of the electronic pen, respectively; alpha is alphax、αyAnd alphazRespectively the angular acceleration component of the electronic pen; a. thex、AyAnd AzAcceleration components at the centroid of the electronic pen, respectively;
and the analytic solutions of the three axial angular velocities of the electronic pen satisfy the following relations:
Figure BDA0002205203710000087
Figure BDA0002205203710000088
in the formula:
Figure BDA0002205203710000089
Figure BDA00022052037100000810
Figure BDA00022052037100000811
Figure BDA0002205203710000091
generally, due to the small installation error angle, the following 3 small rotations can be used for sequentially describing:
Figure BDA0002205203710000092
in the formula:the mounting error angle of each accelerometer can be measured by a multi-position test through a discrete calibration method;
the specific force equation for the twelve accelerometer outputs containing the error is thus expressed as:
Figure BDA0002205203710000095
in actual test, the value on the left side of the above formula is measured by the test system in real time, and the value at any moment is recorded as
Figure BDA0002205203710000096
Namely the above type is changed into
Figure BDA0002205203710000097
This is a mathematical model of the calculated angular velocity including the mounting error, and the instantaneous angular velocity at that time can be obtained from each instantaneous system of solved equations.
Preferably, each accelerometer in the twelve degree-of-freedom configuration map is equidistant or close to the centroid point.
As shown in fig. 2 to 5, an ICA blind source separation method is adopted to obtain the posture parameter information of the electronic pen, and the ICA blind source separation method includes the following steps: firstly, measuring Gaussian characteristics of electronic pen aliasing signals acquired from an electronic pen through fourth-order cumulant, and dividing random variables into a super-Gaussian random variable, namely, a kurtosis is positive, a Gaussian random variable, namely, the kurtosis is zero, and a sub-Gaussian random variable, namely, the kurtosis is negative according to the positive and negative of a kurtosis value, wherein the super-Gaussian signal has a typical 'long-tip' probability density function curve, and the typical super-Gaussian distribution is Laplace distribution; secondly, performing Wavelet decomposition by using Wavelet and combining Principal Component Analysis (PCA), and calculating the number of signal sources; and finally, separating noise signals such as motion signals of the electronic pen, installation error noise and the like through Independent Component Analysis (ICA) to obtain attitude parameter information of the electronic pen.
Further, the calculation of the direction cosine matrix of the mutual transformation between the two coordinate systems is to measure the specific force of the electronic pen in the axial direction of the carrier coordinate system by using the accelerometer, and the output information of the accelerometer needs to be transformed to the navigation coordinate systemNavigation calculation can be carried out, and the matrix required by the transformation is the attitude matrix
Figure BDA0002205203710000098
I.e. a transformation matrix between the carrier coordinate system and the navigation coordinate system,
Figure BDA0002205203710000101
the relative position between the two coordinate systems can be determined with three independent rotation angles, which can be represented by three coordinate rotations in the following order: the first rotation is xnynznAround znPositive rotation of the shaft
Figure BDA0002205203710000102
Angle of arrival xn1yn1zn1A location; the second rotation is xn1yn1zn1Around xn1The shaft being rotated forwardly through an angle theta to xn2yn2zn2A location; the third rotation is xn2yn2zn2Around yn2Is rotated through an angle gamma to xbybzbA location;
Figure BDA0002205203710000103
wherein
Figure BDA0002205203710000104
Theta and gamma are respectively expressed as a heading angle, a pitch angle and a roll angle of the carrier. According to the rotation sequence, a coordinate conversion relation from a navigation coordinate system to a carrier coordinate system can be obtained;
attitude transformation matrix
Figure BDA0002205203710000105
Is the angle of coursePitch angle θ and yawGamma function of roll angle of
Figure BDA0002205203710000107
Can determine
Figure BDA0002205203710000108
θ、γ；
Assume that the directional cosine matrix is represented as:
Figure BDA0002205203710000109
the attitude angle is then:
Figure BDA00022052037100001010
θ＝sin-1(T32)
Figure BDA00022052037100001011
as shown in fig. 6, the electronic pen includes an electronic pen main body, a laser light source 1 is arranged at the bottom of the electronic pen main body, a handwriting switch 3 is arranged at the top of the electronic pen main body 2, a laser switch 2 is arranged on the side surface of the electronic pen main body, an electronic pen processor and a handwriting sensing system are arranged in the electronic pen main body, and the handwriting switch 3, the laser light source 1, the laser switch 2 and the handwriting sensing system are respectively connected with the electronic pen processor.

Claims (6)

1. A handwritten track information acquisition method is characterized by comprising the following steps: the position after the electronic pen switch is turned on is recorded as the initial position S0(ii) a From a starting position S0The inertial information is used as an initial condition, as the electronic pen moves in space, twelve MEMS accelerometers in the electronic pen can calculate the linear acceleration and the angular velocity information of the roll, pitch and course axes of the electronic pen through a handwriting sensing system according to an attitude calculation algorithm embedded in an FPGA in advance, and the electronic pen processor obtains the linear acceleration and the angular velocity information and then obtains the direction cosine at the momentThe matrix differential equation is:
Figure FDA0002205203700000011
Figure FDA0002205203700000012
for three-axis angular velocity omegax、ωy、ωzThe formed anti-symmetric matrix is a matrix with a plurality of anti-symmetric matrixes,
Figure FDA0002205203700000013
a direction cosine matrix for the solution; according to a carrier coordinate system of the electronic pen and a first-order differential matrix of a direction cosine matrix of a geographic coordinate system, solving a direction cosine matrix differential equation in real time to obtain a direction cosine matrix representing the posture of the electronic pen, and then integrating linear acceleration information and updating an equation of the speed of the electronic pen; further integrating the linear acceleration information to deduce the track change displacement of the electronic pen; after the angular acceleration of the roll, the pitch and the course axis is subjected to secondary integration, the angle change of the electronic pen is obtained, so that the track change of the electronic pen is calculated, the attitude parameter information of the electronic pen is obtained in real time, and the track change of the electronic pen is displayed on a two-dimensional screen.
2. The handwritten trajectory information acquisition method according to claim 1, characterized in that the velocity update equation of the electronic pen is a direction cosine matrix update equation, and the direction cosine matrix update equation is:
Figure FDA0002205203700000015
wherein
Figure FDA0002205203700000016
Is [ t ]m-1,tm]Angular increment within a time period and noting the value of delta thetam＝|Δθm|。
3. The handwritten trajectory information acquisition method according to claim 1, wherein the calculation of linear acceleration and angular velocity information of the roll, pitch, and course axes of the electronic pen is performed by using a twelve-degree-of-freedom configuration scheme diagram, the arrow direction corresponding to each digit is the measurement direction of an accelerometer, the O point corresponds to the centroid of the pen, the accelerometer cannot be installed at the centroid, the Z axis is the axis direction of the pen, and the change of the trajectory attitude of the pen holder is measured by using the cantilever effect of the accelerometer;
the sensitive direction of each accelerometer is respectively set as
Figure FDA0002205203700000021
And the installation position of each accelerometer is as follows:
Figure FDA0002205203700000022
the specific force equation for twelve accelerometers is:
f2＝aωzωx-aαy+Az
Figure FDA0002205203700000024
f4＝-aωzωx+aαy+Az
Figure FDA0002205203700000025
f6＝aωzωy-aαx+Az
Figure FDA0002205203700000026
f8＝-aωzωy+aax+Az
Figure FDA0002205203700000027
Figure FDA0002205203700000028
Figure FDA0002205203700000029
Figure FDA00022052037000000210
in the formula: omegax、ωyAnd ωzAre the angular velocity components of the electronic pen, respectively; alpha is alphax、αyAnd alphazRespectively the angular acceleration component of the electronic pen; a. thex、AyAnd AzAcceleration components at the centroid of the electronic pen, respectively;
and the analytic solutions of the three axial angular velocities of the electronic pen satisfy the following relations:
Figure FDA0002205203700000031
Figure FDA0002205203700000032
in the formula:
Figure FDA0002205203700000034
Figure FDA0002205203700000035
Figure FDA0002205203700000036
Figure FDA0002205203700000037
generally, due to the small installation error angle, the following 3 small rotations can be used for sequentially describing:
Figure FDA0002205203700000038
Figure FDA0002205203700000039
in the formula:
Figure FDA00022052037000000310
the mounting error angle of each accelerometer can be measured by a multi-position test through a discrete calibration method;
the specific force equation for the twelve accelerometer outputs containing the error is thus expressed as:
Figure FDA0002205203700000041
in actual test, the value on the left side of the above formula is measured by the test system in real time, and the value at any moment is recorded as
Figure FDA0002205203700000042
Namely the above type is changed into
Figure FDA0002205203700000043
This is a mathematical model of the calculated angular velocity including the mounting error, and the instantaneous angular velocity at that time can be obtained from each instantaneous system of solved equations.
4. The method according to claim 1, wherein each accelerometer in the twelve-degree-of-freedom layout has an equal or similar distance from a centroid point.
5. The method for acquiring handwritten trajectory information according to claim 1, wherein an ICA blind source separation method is adopted for acquiring the posture parameter information of the electronic pen, and the ICA blind source separation method includes the following steps:
firstly, measuring Gaussian characteristics of electronic pen aliasing signals acquired from an electronic pen through fourth-order cumulant, and dividing random variables into a super-Gaussian random variable, namely, a kurtosis is positive, a Gaussian random variable, namely, the kurtosis is zero, and a sub-Gaussian random variable, namely, the kurtosis is negative according to the positive and negative of a kurtosis value, wherein the super-Gaussian signal has a typical 'long-tip' probability density function curve, and the typical super-Gaussian distribution is Laplace distribution; secondly, performing Wavelet decomposition by using Wavelet and combining Principal Component Analysis (PCA), and calculating the number of signal sources; and finally, separating noise signals such as motion signals of the electronic pen, installation error noise and the like through Independent Component Analysis (ICA) to obtain attitude parameter information of the electronic pen.
6. The method for acquiring handwritten locus information according to claim 1, wherein the calculation of the direction cosine matrix of the mutual transformation between the two coordinate systems is performed by using an accelerometer to measure the specific force of the electronic pen in the axial direction of the carrier coordinate system, the navigation calculation is performed only by transforming the output information of the accelerometer to the navigation coordinate system, and the matrix required by the transformation is the matrix required by the transformationIs a matrix of gestures
Figure FDA0002205203700000044
I.e. a transformation matrix between the carrier coordinate system and the navigation coordinate system,
Figure FDA0002205203700000045
the relative position between the two coordinate systems can be determined with three independent rotation angles, which can be represented by three coordinate rotations in the following order: the first rotation is xnynznAround znPositive rotation of the shaft
Figure FDA0002205203700000046
Angle of arrival xn1yn1zn1A location; the second rotation is xn1yn1zn1Around xn1The shaft being rotated forwardly through an angle theta to xn2yn2zn2A location; the third rotation is xn2yn2zn2Around yn2Is rotated through an angle gamma to xbybzbA location;
Figure FDA0002205203700000051
wherein
Figure FDA0002205203700000057
Theta and gamma are respectively expressed as a course angle, a pitch angle and a roll angle of the carrier, and a coordinate conversion relation from a navigation coordinate system to a carrier coordinate system is obtained according to the rotation sequence;
attitude transformation matrix
Figure FDA0002205203700000052
Is the angle of course
Figure FDA0002205203700000059
Gamma functions of pitch angle theta and roll angle, of
Figure FDA0002205203700000053
Can determine
Figure FDA0002205203700000058
θ、γ；
Assume that the directional cosine matrix is represented as:
Figure FDA0002205203700000054
the attitude angle is then:
Figure FDA0002205203700000055
θ＝sin-1(T32)
Figure FDA0002205203700000056
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