TW201407164A - The coordinate transformation method, the calculating method of independent coordinate and the accelerometer detecting system - Google Patents

Abstract

This coordinate system transformation algorithm is applied on an accelerometer. It transforms the acceleration vector provided from accelerometer in a rectangular coordinate system to an independent coordinate system to retrieve the inclination information of the object. This algorithm is first to rotate the acceleration vector around 1<SP>st</SP>-axis and have its projected vector on the plane constructed from the other two axes aligned to the 2<SP>nd</SP>-axis. After that, rotate the acceleration vector on the 1<SP>st</SP>-2<SP>nd</SP>-axes plane, have it aligned on the 2<SP>nd</SP>-axis and calculate the rotation angle to get the 1<SP>st</SP> desired angle between the original acceleration vector and 1<SP>st</SP>-axis of the independent coordinate system. Based on the same concept of vector rotations, the angles between the horizontal plane, which is perpendicular to the acceleration vector, and the 2<SP>nd</SP>-axis and 3<SP>rd</SP>-axis can be calculated respectively. This algorithm can be applied on some clinical applications to detect if the patients or elderly people are trying to get out of bed. It can be also applied on the clinical evaluation of the patient's capability of dynamic posture control.

Description

Coordinate conversion method, calculation method of independent coordinates and acceleration sensing system

The present invention relates to a conversion method, and more particularly to a coordinate conversion method for converting an acceleration vector from a right angle coordinate system to an independent coordinate system to calculate an angular relationship between the acceleration vector and the coordinate axis.

Referring to Figure 1, an acceleration vector sensed by an accelerometer is a vector that falls within the coordinate system (X, Y, Z). If the vector is converted into an independent coordinate system (φ, θ, Ψ ) The acceleration gauge can be obtained corresponding to the orientation of gravity, since the acceleration vector is converted into an angle in the independent coordinate system by the following equations (1)~(3)

However, the operations of multiplication, division, trigonometric function, and opening number are complicated, so the acceleration sensing system used today to calculate the angle (φ, θ, Ψ ) mainly has the following methods: the first way The acceleration vector sensed by the acceleration gauge is stored, and then the operation is performed through the personal computer in an offline manner, and then converted into an angle and then analyzed. The disadvantage of this approach is that the acceleration sensing system cannot perform real-time analysis and judgment.

The second method is to cooperate with the acceleration sensing system through a short-distance wireless transmission module to accelerate the acceleration vector sensed by the acceleration gauge to the electronic device such as a personal computer, a mobile phone, or a PDA by using a wireless transmission module. The calculation and judgment of the angle are performed by using a processor with high computational performance in the devices. This makes the acceleration sensing system need to be realized through the devices, which will reduce the portability of the acceleration sensing system, and the long-term uninterrupted wireless signal transmission, the concern that the electric wave is harmful to the human body, and the cost is high.

The third way is to store the angles corresponding to the conversions of all the acceleration vectors in the acceleration sensing system in advance, so that when the acceleration gauge senses any acceleration vector, the acceleration sensing system can obtain the corresponding by using the look-up table. Angle information, but this approach will require a large amount of memory space to achieve the required accuracy.

Therefore, the object of the present invention is to provide a coordinate conversion method capable of real-time, high accuracy and low computational amount, to calculate an angular relationship between an acceleration vector and a coordinate axis, and an acceleration sensing system using an acceleration gauge. Achieving an instant detection of object tilt angles can be extended to many clinical monitoring and evaluation purposes.

Therefore, the coordinate conversion method of the present invention is applied to an acceleration sensing system for converting an acceleration vector sensed by an acceleration gauge from a right angle coordinate system to an independent coordinate system, wherein the orthogonal coordinate system is a first coordinate axis, Defined by a second coordinate axis and a third coordinate axis, the independent seat The standard system is a first angle between the acceleration vector and the first coordinate axis, and a plane perpendicular to the acceleration vector and a second angle and a third angle respectively of the second coordinate axis and the third coordinate axis, the coordinate conversion The method comprises the following steps: (A) rotating the acceleration vector around the first coordinate axis, causing the component of the acceleration vector projected on the plane formed by the second coordinate axis and the third coordinate axis to overlap the second coordinate axis, and calculating the acceleration vector projected on the The component length on the second coordinate axis, and at this time, the acceleration vector after the rotation also falls on the plane formed by the first coordinate axis and the second coordinate axis; (B) the acceleration vector after the rotation in the step (A) is further The third coordinate axis is centered, and rotates on a plane formed by the first coordinate axis and the second coordinate axis, so that the acceleration vector is superposed on the second coordinate axis, and the acceleration vector is rotated to overlap the angle of the second coordinate axis to obtain a first angle; (C) rotating the acceleration vector around the second coordinate axis, and projecting the acceleration vector on the first coordinate axis and the third coordinate axis The component on the surface overlaps the third coordinate axis, and calculates the component length of the acceleration vector superimposed on the third coordinate axis; (D) the acceleration vector after the rotation in step (C) is centered on the first coordinate axis, and the second coordinate axis And rotating on a plane formed by the third coordinate axis, the acceleration vector is superposed on the third coordinate axis, and the acceleration vector is rotated to overlap the angle of the third coordinate axis to obtain a second angle; (E) the acceleration vector is at the third coordinate axis For center rotation, the component of the acceleration vector projected on the plane formed by the first coordinate axis and the second coordinate axis is overlapped with the first coordinate axis, and the acceleration vector is calculated to overlap the first coordinate The length of the component on the axis; and (F) rotating the acceleration vector after the rotation in the step (E) around the second coordinate axis, and rotating on the plane formed by the first coordinate axis and the third coordinate axis, so that the acceleration vector is superimposed on The first axis is plotted and the acceleration vector is rotated to an angle that overlaps the first coordinate axis to obtain a third angle.

Wherein, the steps (A) and (B), (C) and (D), and the execution sequence of the steps (E) and (F) may be mutually reversed or performed simultaneously.

Further, step (A) includes the following sub-steps: (A-1) rotating the acceleration vector by an angle toward the second coordinate axis about the first coordinate axis, and recording an angle parameter related to the angle; (A- 2) It is determined whether the components of the second coordinate axis and the third coordinate axis corresponding to the acceleration vector are the same as before the rotation, if yes, step (A-5) is performed, and if not, step (A-3) is performed; (A-3) The acceleration vector is rotated by an angle from the first coordinate axis toward the second coordinate axis, the tan value of the angle is half of the tan value of the previous rotation angle, and an angle parameter related to the angle is recorded; (A-4) Repeating steps (A-2) and (A-3) for a specific number of times; and (A-5) multiplying a quantization factor by a component on the second coordinate axis to calculate a post-rotation acceleration vector projected on the second coordinate axis The component length on the top.

Step (B) includes the following substeps: (B-1) rotating the acceleration vector by an angle on a plane formed by the first coordinate axis and the second coordinate axis about the third coordinate axis toward the second coordinate axis, and recording one An angle parameter related to the angle; (B-2) determining whether the component of the acceleration vector corresponding to the first coordinate axis is zero, and if so, performing step (B-5), if not, performing step (B-3); (B-3) performing the acceleration vector The third coordinate axis is rotated at an angle to the center of the second coordinate axis, and the tan value of the angle is half of the tan value of the previous rotation angle, and an angle parameter related to the angle is recorded; (B-4) repeating the steps (B-2) and (B-3) for a specific number of times; (B-5) add all the angle parameters of the record to obtain a rotation angle related to the first angle, and then go through step (B) The acceleration vector of the rotation will fall on the second coordinate axis; and (B-6) the first angle is obtained by subtracting the rotation angle by π/2.

In addition, if you need to obtain the acceleration vector The length is in step (B-2), and if it is zero, the recording of all the following rotation angle parameters is stopped, but step (B-3) is repeatedly executed for a certain number of times, and finally a quantization factor is The original length of the acceleration vector can be calculated by multiplying the components on the second coordinate axis.

In addition, step (C) includes the following sub-steps: (C-1) rotating the acceleration vector about an angle of the second coordinate axis toward the third coordinate axis, and recording an angle parameter related to the angle; (C- 2) Determine whether the acceleration vector corresponds to the component of the third coordinate axis and the first coordinate axis is the same as before the rotation, if yes, execute step (C-5), if not, perform step (C-3); (C-3) The acceleration vector is rotated by an angle from the second coordinate axis toward the third coordinate axis, and the tan value of the angle is the previous rotation angle. Half of the tan value, and record an angle parameter related to the angle; (C-4) repeat steps (C-2) and (C-3) for a specific number of times; and (C-5) a quantization factor The components on the third coordinate axis are multiplied to calculate the component length of the rotated acceleration vector projected on the third coordinate axis.

Step (D) includes the following sub-steps: (D-1) rotating the acceleration vector by an angle on a plane formed by the second coordinate axis and the third coordinate axis about the first coordinate axis toward the third coordinate axis, and recording one An angle parameter related to the angle; (D-2) determining whether the component of the second coordinate axis corresponding to the acceleration vector is zero, and if so, performing step (D-5), and if not, performing step (D-3); -3) rotating the acceleration vector to an angle close to the third coordinate axis centering on the first coordinate axis, the tan value of the angle is half of the tan value of the previous rotation angle, and recording an angle parameter related to the angle; -4) Repeat steps (D-2) and (D-3) for a specific number of times; and (D-5) add the angle parameters of all the records to calculate the second angle.

In addition, step (E) includes the following sub-steps: (E-1) rotating the acceleration vector to an angle close to the first coordinate axis centering on the third coordinate axis, and recording an angle parameter related to the angle; (E- 2) judging whether the acceleration vector corresponds to the component of the first coordinate axis and the second coordinate axis is the same as before the rotation, if yes, executing step (E-5), if not, performing step (E-3); (E-3) The acceleration vector is rotated at an angle close to the first coordinate axis centering on the third coordinate axis, and the tan value of the angle is the previous rotation angle. Half of the tan value, and record an angle parameter related to the angle; (E-4) repeat steps (E-2) and (E-3) for a specific number of times; and (E-5) a quantization factor The components on the first target axis are multiplied to calculate the component length of the rotated acceleration vector projected on the first coordinate axis.

Step (F) includes the following sub-steps: (F-1) rotating the acceleration vector by an angle on a plane formed by the first coordinate axis and the third coordinate axis about the second coordinate axis toward the first coordinate axis, and recording one Angle parameter related to the angle; (F-2) determining whether the component of the acceleration coordinate vector corresponding to the third coordinate axis is zero, if yes, executing step (F-5), and if not, performing step (F-3); -3) rotating the acceleration vector to an angle close to the first coordinate axis centering on the second coordinate axis, the tan value of the angle is half of the tan value of the previous rotation angle, and recording an angle parameter related to the angle; -4) Repeat steps (F-2) and (F-3) for a specific number of times; and (F-5) add the angle parameters of all the records to calculate the third angle.

Further, another object of the present invention is to provide an acceleration sensing system that can perform the above-described coordinate conversion method.

The acceleration sensing system of the present invention comprises a sensing unit (acceleration gauge), a vector rotation unit coupled to the sensing unit, and a computing unit coupled to the vector rotation unit.

The sensing unit (acceleration gauge) is configured to generate an acceleration vector according to its own motion, the acceleration vector is presented by a right angle coordinate system, and the orthogonal coordinate system is a first coordinate axis and a second coordinate axis perpendicular to each other. And a third coordinate axis is defined.

Wherein, the vector rotation unit first rotates the acceleration vector around the first coordinate axis, and the component of the acceleration vector projected on the plane formed by the second coordinate axis and the third coordinate axis overlaps the second coordinate axis, and the calculation unit calculates the acceleration vector to be projected on a component length on the second coordinate axis, the vector rotation unit rotates the rotated acceleration vector around the third coordinate axis, and rotates on a plane formed by the first coordinate axis and the second coordinate axis, so that the acceleration vector overlaps the second coordinate axis. And the calculating unit calculates the angle at which the acceleration vector is rotated to overlap the second coordinate axis. In addition, the acceleration sensing system further includes an angle adjusting unit coupled to the calculating unit, and subtracting the angle calculated by the calculating unit by using π/2 to obtain The first angle of the acceleration vector and the first coordinate axis.

The vector rotation unit also rotates the acceleration vector around the second coordinate axis, so that the component of the acceleration vector projected on the plane formed by the first coordinate axis and the third coordinate axis overlaps the third coordinate axis, and the calculation unit calculates the acceleration vector to be projected in the third The component length on the coordinate axis, the vector rotation unit rotates the above-mentioned rotated acceleration vector on the plane formed by the second coordinate axis and the third coordinate axis centering on the first coordinate axis, so that the acceleration vector is superimposed on the third coordinate axis, and the calculation is performed. The unit calculates the acceleration vector to rotate to an angle overlapping the third coordinate axis to obtain a second angle between the plane perpendicular to the acceleration vector and the second coordinate axis; the vector rotation unit also rotates the acceleration vector around the third coordinate axis to make the acceleration vector a component projected on a plane formed by the first coordinate axis and the second coordinate axis overlaps the first coordinate axis, and the calculation unit calculates a component length of the acceleration vector projected on the first coordinate axis, and the vector rotation unit The rotated acceleration vector is further rotated on a plane formed by the first coordinate axis and the third coordinate axis centered on the second coordinate axis, so that the acceleration vector is superposed on the first coordinate axis, and the calculation unit calculates the acceleration vector to rotate to overlap the first coordinate axis. The angle is a third angle between the plane perpendicular to the acceleration vector and the third coordinate axis.

Furthermore, another object of the present invention is to apply to the conversion of independent coordinates using a polar coordinate calculation method.

The calculation method is performed by an electronic device to calculate a polar coordinate of a vector located in a plane rectangular coordinate system. The plane rectangular coordinate system includes a first coordinate axis and a second coordinate axis, and the vector forms a first component and a second component corresponding to the first coordinate axis and the second coordinate axis, and the calculation method comprises the following steps: (A) placing the vector close to the first The direction of one of the axes is rotated by an angle, and an angle parameter related to the angle is recorded; (B) determining whether the first component and the second component of the vector are the same as before the rotation, and if so, performing step (E), if not, Further determining whether the second component is zero, and if so, stopping recording of all subsequent rotation angle parameters; (C) rotating the vector by an angle in a direction close to the first coordinate axis, and the tan value of the angle is the previous rotation angle Half of the tan value, and record an angle parameter related to the angle; (D) repeat steps (B) and (C) for a specific number of times; and (E) add all the angle parameters of the record to obtain the vector and The angle between the first axis.

The calculation method may further comprise a step (F) after the step (E), The length of the vector is calculated from the component of the first coordinate axis in step (E). In detail, the step (F) is to calculate the original length of the vector by multiplying the component of the first coordinate axis in the step (E) by a quantization factor.

However, the quantization factor is a fixed constant, so multiplication with the quantization factor can be disassembled into a series of displacements and additions and subtractions, so that the present invention can avoid complex multiplication and division by the concept of vector rotation and the iterative operation approximation. The calculation of the root number and trigonometric functions achieves immediate, low cost, low power consumption and low computational efficiency.

Specifically, in step (B), it is first determined whether the first and second components of the rotated vector are the same as before the rotation. If they are the same, then if the step (C) is repeated, the vector is rotated and then There will be no changes, so the iteration operation can be stopped and step (E) is performed. In this way, on the one hand, the iterative operation can be ended early, and on the other hand, the continual accumulation of the angle parameters can be avoided, resulting in an increase in the final calculated angle error.

If the judgment is different, it is determined whether the second component of the rotated vector is zero. If so, then the vector has just overlapped on the first coordinate axis, and the sum of the currently recorded rotation angle parameters is exactly the initial vector. The angle with the first coordinate axis, so the record of all subsequent rotation angle parameters is stopped. If it is only necessary to calculate the angle between the vector and the first coordinate axis, step (E) can be performed, and then the calculation ends. However, if it is necessary to calculate the original length of the vector, since the specific number of iterations must be executed in step (F) to use the specific quantization factor, in order to avoid the rotation angle parameter in the post-heap generation is continuously accumulated. Resulting in an increase in the error of the angle calculated in the last step (E), so stop all the parameters of the rotation angle Recorded, but the iteration operation continues until a specific number of times.

The above and other technical contents, features and advantages of the present invention will be apparent from the following detailed description of the preferred embodiments.

Referring to FIG. 1 and FIG. 2, a preferred embodiment of the acceleration sensing system of the present invention is an acceleration vector sensed by the concept of "vector rotation". Convert from a constant-angle coordinate system (X, Y, Z) to an independent coordinate system (φ, θ, Ψ ), and use simple addition and subtraction and displacement operations, with Iterative Operations, in an approximation manner, Acceleration vector The length and its angle of rotation to obtain the azimuth angle of the sensing unit (acceleration gauge) 10 with respect to the gravity, thus avoiding the complicated calculation of multiplication and division, opening number, and trigonometric function to reduce cost and Computation.

In this embodiment, the rectangular coordinate system is defined by a first coordinate axis (Z axis), a second coordinate axis (X axis), and a third coordinate axis (Y axis) perpendicular to each other, and the independent coordinate system is composed of an acceleration vector. One of the first angle φ and acceleration vector sandwiched by the first coordinate axis (Z axis) The second angle θ and the acceleration vector of the vertical plane and the second coordinate axis (X axis) The vertical plane is formed by a third angle Ψ between the third coordinate axis (Y axis).

The angles of the first angle φ, the second angle θ, and the third angle Ψ are defined as follows:

The acceleration sensing system 100 includes a sensing unit 10, a vector rotation unit 20, a calculation unit 30, and an angle adjustment unit 40. The sensing unit 10 is an accelerometer for sensing an acceleration vector according to its own motion. The vector rotation unit 20 is coupled to the sensing unit 10 for making the acceleration vector Rotating around any coordinate axis; computing unit 30 is coupled to vector rotation unit 20 for calculating acceleration vector Component length on any coordinate axis, and vector rotation unit 20 rotation acceleration vector The angle adjustment unit 40 is coupled to the calculation unit 30 for adjusting the rotation angle calculated by the calculation unit 30 so as to satisfy the angular range of the independent coordinate system.

Referring to FIG. 3, how the acceleration sensing system 100 of the present embodiment uses the addition and subtraction method and the displacement operation to achieve the acceleration vector will be described in detail below. Coordinate transformation and inclination calculation.

In step S10, the sensing unit 10 senses an acceleration vector generated according to the acceleration gauge motion. And acceleration vector It is represented by ( A _X , A _Y , A _Z ) coordinates on the Cartesian coordinate system.

Step S20, the vector rotation unit 20 will accelerate the vector Rotating around the first coordinate axis (Z axis), as shown in Figure 4, making the acceleration vector The component projected on the XY plane overlaps the second coordinate axis (X axis) and forms a new acceleration vector , its position coordinates are (A' _X , 0, A _Z ), at this time, the acceleration vector after rotation Will fall on the plane formed by the XZ axis, and the calculation unit 30 will calculate the acceleration vector The component length |A' _X | projected on the second coordinate axis (X-axis).

Acceleration vector Rotating only with the first coordinate axis (Z axis) axis, its own vector length does not change, relatively, the acceleration vector The length of the component projected on the XY plane is also not affected by the acceleration vector. The rotation is increased or decreased, so the acceleration vector after rotation The component length |A' _X | projected on the XY plane will be equal to the original acceleration vector Component length projected on the XY plane .

Step S30, the vector rotation unit 20 will accelerate the vector Then rotate around the third coordinate axis (Y axis) (ie the acceleration vector on the XZ plane) Approaching the X axis), as shown in Figure 5, to make the acceleration vector Overlap on the second coordinate axis (X-axis) and form a new acceleration vector , whose position coordinates are (A" _X , 0, 0), and the calculation unit 30 calculates the acceleration vector The angle δ is rotated to overlap the X-axis, and the angle δ is subtracted from the angle δ by the angle adjusting unit 40 to obtain the first angle φ.

However, in steps S20 and S30, the calculation unit 30 calculates the length of the vector and its rotation angle in a manner of approximating the iteration. In the two-dimensional coordinates, an initial vector V _{0 is} given with a coordinate of [X ₀ , Y ₀ ]. If this vector is rotated by an angle τ to become a new vector V, and its coordinate is [X', Y'], it can be expressed by equation (1), that is, the acceleration vector. The angle of rotation on the XY plane and the length of the component projected on the second coordinate axis (X-axis) can be obtained by the array operation of equation (1).

In this embodiment, the rotation basic angle τ _i (-π/2 ≦ τ _i ≦ π/2) in the iterative operation of the ith is set such that the tan value is 2 ^{- i} , that is, tan (τ _i )=2 ^{- i} . Therefore, after i iterations, the final vector coordinate value [X, Y] is as in equation (2).

The value of d _i in equation (2) depends on the value of Y _i in the i-th iteration. If Y _i <0, then d _i =1, that is, the [ X _i , Y _i ] vector is counterclockwise. Rotation angle τ _i , otherwise d _i == -1, that is, the [ X _i , Y _i ] vector is rotated by the angle τ _i in a clockwise direction. It can be seen from equation (2) that tan(τ _i ) has been selected by the special basic angle τ _i , and the product of its value and the original coordinate value can be converted into a binary displacement and addition and subtraction. In addition, in order to avoid the multiplication of the trigonometric function, in each iteration, only the matrix product part in equation (2) is calculated, as shown in equation (3), and the product of the cos portion is as shown in equation (4). :

Among them, 1/K is called a scaling factor, and it can be known from equation (3) that only the addition and subtraction and the binary displacement operation are needed in each iterative operation to replace the high complexity rooting. Number and trigonometric function calculation. In addition, when the number of iterations is large enough, the quantization factor will be close to a constant value, ie 0.6073, so as long as the quantization factor is decomposed into a series of displacements and additions and subtractions, the vector obtained after j iterations is multiplied. The value, you can know the new vector V. After j-time iteration operations, the approximation of the angle between the initial vector V ₀ and the X-axis is the sum of the rotation angle parameters in each iteration, as shown in (5):

Therefore, referring to FIG. 1, FIG. 4 and FIG. 6, according to the above description, the detailed flow of step S20 of the present embodiment is as follows: step S21, the vector rotation unit 20 will accelerate the vector. An angle τ (starting at 45 degrees) is rotated toward the second coordinate axis (X axis) centering on the first coordinate axis (Z axis), and the calculation unit 30 records an angle parameter related to the angle. Specifically, the calculation unit 30 uses its built-in memory (not shown) to record the fixed angle parameter τ _{i of} each rotation in the iteration, but it can also be stored by using additional memory. The examples are limited.

In step S22, the vector rotation unit 20 determines the rotated acceleration vector. Whether the components of the second coordinate axis (X axis) and the third coordinate axis (Y axis) are the same as before the rotation, if not, it means that the vector rotation has not yet converged, so step S23 is performed; if so, it means that after the vector is rotated, There is no change, so the iterative operation can be stopped, so skip to step S25.

Step S23, the vector rotation unit 20 will accelerate the vector Rotating an angle near the second coordinate axis (X axis) about the first coordinate axis (Z axis), and the tan value of the angle is half of the tan value of the previous rotation angle, and the calculation unit 30 records one and Angle related angle parameters.

In step S24, the vector rotation unit 20 determines whether steps S22 and S23 are repeatedly executed for a certain number of times, and if so, proceeds to step S25; otherwise, returns to step S22. Preferably, the specific number of times is eight, that is, the vector rotation unit 20 performs up to eight iteration operations. Specifically, steps S21 to S24 are the matrix product portions in the calculation formula (2).

In step S25, the calculation unit 30 multiplies the quantization factor (0.6073) by the component on the second coordinate axis (X-axis) obtained by the last iteration in step S23 to obtain the acceleration vector after the rotation. The length of the component projected on the second coordinate axis (X-axis).

Thus, since the tan value of the angle of each iteration is the previous 1/2, the calculation unit 30 can be completed by the binary shifter, which can avoid complicated multiplication and division, opening root number, and trigonometric function. In the calculation, the acceleration sensing system 100 does not need an expensive precision controller, and a large amount of memory space, so the acceleration sensing system 100 will have low cost, low power consumption and low computational efficiency, and the vector rotation Unit 20 is provided with a mechanism to stop the iterative operation (as in step S20) to improve the accuracy of the angle calculation and to avoid accumulation of errors.

Similarly, in step S30, the acceleration vector is also calculated in the manner of iterative operation approximation. Rotating to the angle δ of the overlapping second coordinate axis (X axis), referring to FIG. 1, FIG. 5 and FIG. 7, the detailed flow of step S30 of this embodiment is as follows: step S31, the vector rotation unit 20 will accelerate the vector. Rotating an angle τ (starting at 45 degrees) in a direction close to the second coordinate axis (X axis) on the plane formed by the XZ axis centering on the third coordinate axis (Y axis), and the calculation unit 30 records the angle The relevant angle parameters.

In step S32, the vector rotation unit 20 determines the acceleration vector after the rotation. Whether the component of the first coordinate axis (Z axis) is zero, and if not, the acceleration vector Since it is not overlapped with the second coordinate axis (X axis), step S33 is performed; if yes, step S35 is performed. Supplementary note is the acceleration vector after the turn When the component of the first coordinate axis (Z axis) is zero, then Overlapped on the X-axis, the sum of the currently recorded rotation angle parameters has been the acceleration vector With the angle δ of the second coordinate axis (X-axis), the iterative operation can be stopped and step S35 is executed.

Step S33, the vector rotation unit 20 will accelerate the vector Rotating an angle near the second coordinate axis (X axis) about the third coordinate axis (Y axis), and the tan value of the angle is half of the tan value of the previous rotation angle, and the calculation unit 30 records one and Angle related angle parameters.

In step S34, the vector rotation unit 20 determines whether steps S42 and S43 are repeatedly executed for a certain number of times (again, 8 times). If the specific number of times is reached, step S35 is performed; if the specific number of times is not reached, step S32 is returned.

In step S35, the calculating unit 30 adds all the recorded angle parameters to obtain the rotation angle δ related to the first angle φ, and then the acceleration vector rotated through the steps S31 to S34. Will fall on the second coordinate axis (X axis).

In particular, as shown in Figure 5, the acceleration vector will be known. The angle δ rotated to overlap the second coordinate axis (X axis) is added to the first angle φ constituting the independent coordinate system to be π/2, so that the angle adjusting unit 40 subtracts the rotation angle δ by π/2 in step S36. The first angle φ is calculated. In addition, if you need to obtain the acceleration vector In the step S32, if it is zero, the recording of all the rotation angle parameters is stopped, but the step S33 is repeated for a certain number of times, and finally the calculation unit 30 is used to calculate the quantization factor (0.6073) and the step S33. The acceleration vector can be calculated by multiplying the components on the X-axis obtained by the last iteration. The original length.

In addition, the discrimination of step S22, when the vector rotation has converged (ie, the coordinate components before and after the rotation are the same), the iterative operation can be ended early, and on the other hand, the continual accumulation of the angle parameters can be avoided to cause the final calculated angle error to increase. . In addition, even if the rotation has not yet converged, just after the vector is rotated and overlapped with the first coordinate axis (Z axis) (ie, step S32), the recording of all the rotation angle parameters or the stop iteration operation is stopped, so as to obtain the most accurate. The angle between the vector and the first coordinate axis (Z axis)

Referring back to FIGS. 1 and 3, the second angle θ of the independent coordinate system can also be obtained through steps S40 and S50.

Step S40, the vector rotation unit 20 will accelerate the vector Rotating around the second coordinate axis (X axis), making the acceleration vector The component projected on the YZ plane overlaps the third coordinate axis (Y axis) and forms a new acceleration vector , its position coordinates are (A _X , A ' _Y , 0), at this time, the acceleration vector after rotation Will fall on the plane formed by the XY axis, and the calculation unit 30 will calculate the acceleration vector The component length |A' _Y | projected on the third coordinate axis (Y axis).

In step S50, the vector rotation unit 20 will accelerate the vector. Rotate around the first coordinate axis (Z axis) (ie, the acceleration vector on the XY plane) Approaching the Y axis), making the acceleration vector Overlap on the third coordinate axis (Y-axis) and form a new acceleration vector , whose position coordinates are (0, A" _Y , 0), and the calculation unit 30 calculates the acceleration vector The second angle θ is obtained by rotating to an angle overlapping the third coordinate axis (Y axis).

The second angle θ also uses the iterative operation to calculate the acceleration vector in an approximation manner. The length and its angle of rotation. Therefore, referring to FIG. 1 and FIG. 8, the detailed flow of step S40 of this embodiment is as follows: step S41, the vector rotation unit 20 will accelerate the vector. An angle τ (starting at 45 degrees) is rotated toward the third coordinate axis (Y axis) centering on the second coordinate axis (X axis), and the calculation unit 30 records an angle parameter related to the angle.

In step S42, the vector rotation unit 20 determines the rotated acceleration vector. Whether the components of the third coordinate axis (Y axis) and the first coordinate axis (Z axis) are the same as before the rotation, if not, it means that the vector rotation has not converged, so step S43 is performed; if so, it means that after the vector is rotated, There is no change, so the iterative operation can be stopped, and the process jumps to step S45.

Step S43, the vector rotation unit 20 will accelerate the vector Rotating an angle near the third coordinate axis (Y axis) about the second coordinate axis (X axis), and the tan value of the angle is half of the tan value of the previous rotation angle, and the calculation unit 30 records one and Angle related angle parameters.

In step S44, the vector rotation unit 20 determines whether steps S42 and S43 are repeatedly executed for a certain number of times (eight times). If the specific number of times is reached, step S45 is performed; if the specific number of times is not reached, step S42 is returned.

In step S45, the calculating unit 30 multiplies the quantization factor (0.6073) by the component on the third coordinate axis (Y-axis) obtained by the last iteration in step S43 to obtain the rotated acceleration vector. The component length projected on the third coordinate axis (Y axis).

Referring to FIG. 1 and FIG. 9, the detailed flow of step S50 is as follows: in step S51, the vector rotation unit 20 will accelerate the vector. Rotating an angle τ (starting at 45 degrees) in a direction near the third coordinate axis (Y axis) on the plane formed by the XY axis centering on the first coordinate axis (Z axis), and the calculation unit 30 records the angle The relevant angle parameters.

In step S52, the vector rotation unit 20 determines the acceleration vector after the rotation. Whether the component of the second coordinate axis (X axis) is zero, if not, the acceleration vector Since it is not overlapped with the third coordinate axis (Y axis), step S53 is performed; if yes, step S55 is performed. Supplementary note is the acceleration vector after the turn When the component of the second coordinate axis (X axis) is zero, then Overlapped on the Y-axis, the sum of the currently recorded rotation angle parameters is already the acceleration vector With the angle of the third coordinate axis (Y axis), the iterative operation can be stopped and step S55 is performed.

Step S53, the vector rotation unit 20 will accelerate the vector Rotating an angle near the third coordinate axis (Y axis) about the first coordinate axis (Z axis), and the tan value of the angle is half of the tan value of the previous rotation angle, and the calculation unit 30 records one and Angle related angle parameters.

In step S54, the vector rotation unit 20 determines whether steps S52 and S53 are repeatedly executed for a certain number of times (eight times). If the specific number of times is reached, step S55 is performed; if the specific number of times is not reached, the process returns to step S52.

In step S55, the calculation unit 30 adds all the recorded angle parameters to calculate the second angle θ.

Referring back to FIGS. 1 and 3, the third angle Ψ of the independent coordinate system can also be obtained through steps S60 and S70.

In step S60, the vector rotation unit 20 will accelerate the vector. Rotate around the third coordinate axis (Y axis) to make the acceleration vector The component projected on the XZ plane overlaps the first coordinate axis (Z axis) and forms a new acceleration vector , its position coordinates are (0, A _Y , A ' _Z ), at this time, the acceleration vector after rotation Will fall on the plane formed by the YZ axis, and the calculation unit 30 will calculate the acceleration vector The component length |A' _Z | projected on the first coordinate axis (Z axis).

Step S70, the vector rotation unit 20 will accelerate the vector Then rotate around the second coordinate axis (X axis) (ie, the acceleration vector on the YZ plane) Approaching the Z axis), making the acceleration vector Overlap on the first coordinate axis (Z axis) and form a new acceleration vector , whose position coordinates are (0, 0, A" _Z ), and the calculation unit 30 calculates the acceleration vector The third angle Ψ is obtained by rotating to an angle overlapping the first coordinate axis (Z axis).

Similarly, the third angle Ψ is to calculate the acceleration vector in an approximation manner using an iterative operation. The length and its angle of rotation. Therefore, referring to FIG. 1 and FIG. 10, the detailed process of step S60 of this embodiment is as follows:

Step S61, the vector rotation unit 20 will accelerate the vector The angle τ (starting at 45 degrees) is rotated toward the first coordinate axis (Z axis) centering on the third coordinate axis (Y axis), and the calculation unit 30 records an angle parameter related to the angle.

Step S62, the vector rotation unit 20 determines the rotated acceleration vector. Whether the components of the first coordinate axis (Z axis) and the second coordinate axis (X axis) are the same as before the rotation, if not, it means that the vector rotation has not converged, so step S63 is performed; if so, it means that after the vector is rotated, There is no change, so the iterative operation can be stopped, and the process jumps to step S65.

Step S63, the vector rotation unit 20 will accelerate the vector Rotating an angle near the first coordinate axis (Z axis) about the third coordinate axis (Y axis), and the tan value of the angle is half of the tan value of the previous rotation angle, and the calculation unit 30 records one and Angle related angle parameters.

In step S64, the vector rotation unit 20 determines whether steps S62 and S63 are repeatedly executed for a certain number of times (eight times). If the specific number of times is reached, step S65 is performed; if the specific number of times is not reached, the process returns to step S62.

In step S65, the calculating unit 30 multiplies the quantization factor (0.6073) by the component on the first coordinate axis (Z-axis) obtained by the last iteration in step S63 to obtain the rotated acceleration vector. The length of the component projected on the first coordinate axis (Z axis).

Referring to FIG. 1 and FIG. 11, the detailed flow of step S70 is as follows: step S71, the vector rotation unit 20 will accelerate the vector. Rotating an angle τ (starting at 45 degrees) in a direction close to the first coordinate axis (Z axis) on the plane formed by the YZ axis centering on the second coordinate axis (X axis), and the calculation unit 30 records the angle The relevant angle parameters.

Step S72, the vector rotation unit 20 determines the acceleration vector after the rotation Whether the component of the third coordinate axis (Y axis) is zero, and if not, the acceleration vector Since it is not overlapped with the first coordinate axis (Z axis), step S73 is performed; if yes, step S75 is performed. Supplementary note is the acceleration vector after the turn When the component of the third coordinate axis (Y axis) is zero, then Overlapped on the Z axis, the sum of the currently recorded rotation angle parameters is already the acceleration vector With the angle of the first coordinate axis (Z axis), the iterative operation can be stopped and step S75 is performed.

Step S73, the vector rotation unit 20 will accelerate the vector Rotating an angle near the first coordinate axis (Z axis) about the second coordinate axis (X axis), and the tan value of the angle is half of the tan value of the previous rotation angle, and the calculation unit 30 records one and the other Angle related angle parameters.

In step S74, the vector rotation unit 20 determines whether steps S72 and S73 are repeatedly executed for a certain number of times (eight times). If the specific number of times is reached, step S75 is performed; if the specific number of times is not reached, then step S72 is returned.

In step S75, the calculating unit 30 adds all the recorded angle parameters to calculate the third angle Ψ .

Therefore, through the calculation of the first angle φ, the second angle θ, and the third angle Ψ , the acceleration sensing system 100 can know the orientation corresponding to the gravity, and can be applied to medical care, for example, The posture discrimination, the monitoring of the head angle, the detection and judgment of the fall, etc., can be appropriately disposed or prevented immediately.

In summary, the acceleration sensing system 100 uses the concept of "vector rotation" to match the orientation of the gravity and the horizontal plane (the first angle φ, the second angle θ, and the manner of the iterative operation approximation). The third angle Ψ ) can avoid complicated calculation of multiplication and division, opening number, and trigonometric function to reduce cost, power consumption and calculation amount, so that the object of the present invention can be achieved.

However, the above is only the preferred embodiment of the present invention, and the scope of the present invention cannot be limited thereto, that is, the patent application according to the present invention The scope of the invention and the equivalent equivalents and modifications of the invention are still within the scope of the invention.

S10~S70‧‧‧Steps

S21~S25‧‧‧Steps

S31~S36‧‧‧Steps

S41~S45‧‧‧Steps

S51~S55‧‧‧Steps

S61~S65‧‧‧Steps

S71~S75‧‧‧Steps

100‧‧‧Acceleration sensing system

10‧‧‧Sensor unit

20‧‧‧Vector Rotation Unit

30‧‧‧Computation unit

40‧‧‧Angle adjustment unit

1 is a schematic diagram showing acceleration vectors respectively located in a rectangular coordinate system and an independent coordinate system; FIG. 2 is a preferred embodiment of the acceleration sensing system of the present invention; FIG. 3 is a flow chart illustrating a method for calculating the inclination angle of the present invention; Is the acceleration vector Rotate around the Z axis so that the component projected on the XY plane overlaps the X axis to get another vector Figure 5 is an illustration of the acceleration vector Rotating on the XZ plane centered on the Y axis, overlapping it with the X axis to get another vector Figure 6 is an illustration of the acceleration vector Rotating around the Z axis, the component whose projection on the XY plane is superimposed on the X axis; Figure 7 is an illustration of the acceleration vector The process of rotating on the XZ plane centering on the Y-axis to overlap the X-axis; Figure 8 is an illustration of the acceleration vector Rotating around the X axis, the component whose projection on the YZ plane is superimposed on the Y axis; Figure 9 is an illustration of the acceleration vector The process of rotating on the XY plane centering on the Z axis and superimposing it on the Y axis; FIG. 10 is an illustration of the acceleration vector Rotating around the Y-axis, the component whose projection on the XZ plane is superimposed on the Z-axis; and Figure 11 is an illustration of the acceleration vector The process of rotating on the YZ plane centering on the X-axis and superimposing it on the Z-axis.

S10~S70‧‧‧Steps

Claims (13)

A coordinate conversion method is applied to an acceleration sensing system for converting an acceleration vector sensed by the acceleration sensing system from a right angle coordinate system to an independent coordinate system, wherein the orthogonal coordinate system is a first coordinate axis, a second coordinate axis and a third coordinate axis defined by the first angle of the acceleration vector and the first coordinate axis, and a plane perpendicular to the acceleration vector and the second coordinate axis and the The second coordinate axis has a second angle and a third angle. The coordinate conversion method comprises the following steps: (A) rotating the acceleration vector around the first coordinate axis, and projecting the acceleration vector on the second coordinate axis And a component on a plane formed by the third coordinate axis overlaps the second coordinate axis, and calculates a component length of the acceleration vector superimposed on the second coordinate axis; (B) an acceleration vector after the rotation in the step (A) And rotating on the plane formed by the first coordinate axis and the second coordinate axis centering on the third coordinate axis, so that the acceleration vector is heavy And the second coordinate axis is calculated, and the acceleration vector is rotated to overlap the angle of the second coordinate axis to obtain the first angle; (C) the acceleration vector is rotated around the second coordinate axis, and the acceleration vector is projected on the a component on a plane formed by the first target axis and the third coordinate axis overlaps the third coordinate axis, and calculates a component length of the acceleration vector superimposed on the third coordinate axis; (D) after rotating in the step (C) The acceleration vector is further centered on the first coordinate axis, and is formed by the second coordinate axis and the third coordinate axis Rotating in a plane such that the acceleration vector is superimposed on the third coordinate axis, and calculating the acceleration vector to rotate to an angle overlapping the third coordinate axis to obtain the second angle; (E) using the acceleration vector as the third coordinate axis Center-rotating such that a component of the acceleration vector projected on a plane formed by the first coordinate axis and the second coordinate axis overlaps the first coordinate axis, and calculates a component length of the acceleration vector superimposed on the first coordinate axis; and F) rotating the acceleration vector in the step (E) further on the second coordinate axis and rotating on the plane formed by the first coordinate axis and the third coordinate axis, so that the acceleration vector is superposed on the first coordinate axis And calculating the acceleration vector to rotate to an angle overlapping the first coordinate axis to obtain the third angle. The coordinate conversion method according to claim 1, wherein the step (A) comprises the following substeps: (A-1) the acceleration vector is oriented in the direction of the second coordinate axis centering on the first coordinate axis Rotate an angle and record an angle parameter related to the angle; (A-2) determine whether the acceleration vector corresponds to whether the components of the second coordinate axis and the third coordinate axis are the same as before the rotation, and if yes, perform the step (A- 5), if not, performing step (A-3); (A-3) rotating the acceleration vector by an angle toward the second coordinate axis about the first coordinate axis, the tan value of the angle is Half of the tan value of the secondary rotation angle, and record an angle parameter related to the angle; (A-4) repeating steps (A-2) and (A-3) for a specific number of times; and (A-5) multiplying a quantization factor by a component on the second coordinate axis to calculate the rotation The acceleration vector projects the component length on the second coordinate axis. The coordinate conversion method according to claim 1 or 2, wherein the step (B) comprises the following substep: (B-1) the acceleration vector is centered on the first coordinate axis on the first coordinate axis and The plane formed by the second coordinate axis is rotated by an angle toward the second coordinate axis, and an angle parameter related to the angle is recorded; (B-2) determining whether the acceleration vector corresponds to the component of the first coordinate axis Zero, if yes, perform step (B-5), if not, perform step (B-3); (B-3) rotate the acceleration vector around the third coordinate axis toward the second coordinate axis At an angle, the tan value of the angle is half of the tan value of the previous rotation angle, and an angle parameter related to the angle is recorded; (B-4) steps (B-2) and (B-3) are repeatedly performed. a specific number of times; (B-5) adding all the angular parameters of the record to obtain a rotation angle related to the first angle, and the acceleration vector of the rotation will fall on the second coordinate axis; and (B-6 The first angle is calculated by subtracting the rotation angle by π/2. According to the coordinate conversion method of claim 1, wherein the step (C) comprises the following sub-steps: (C-1) rotating the acceleration vector to an angle close to the third coordinate axis about the second coordinate axis, and recording an angle parameter related to the angle; (C-2) determining that the acceleration vector corresponds to Whether the component of the third coordinate axis and the first coordinate axis is the same as before the rotation, if yes, performing step (C-5), if not, performing step (C-3); (C-3) performing the acceleration vector The second coordinate axis is rotated at an angle to a direction close to the third coordinate axis, and the tan value of the angle is half of the tan value of the previous rotation angle, and an angle parameter related to the angle is recorded; (C-4) repeats Performing steps (C-2) and (C-3) for a specific number of times; and (C-5) multiplying a quantization factor by a component on the third coordinate axis to calculate that the rotated acceleration vector is projected on the The component length on the third coordinate axis. The coordinate conversion method according to claim 1 or 4, wherein the step (D) comprises the following substep: (D-1) the acceleration vector is centered on the second coordinate axis on the first coordinate axis and The plane formed by the third coordinate axis is rotated by an angle close to the third coordinate axis, and an angle parameter related to the angle is recorded; (D-2) determining whether the acceleration vector corresponds to the component of the second coordinate axis Zero, if yes, perform step (D-5), if not, perform step (D-3); (D-3) approach the acceleration vector with the first coordinate axis as the center The direction of the third coordinate axis is rotated by an angle, the tan value of the angle is half of the tan value of the previous rotation angle, and an angle parameter related to the angle is recorded; (D-4) repeating the step (D-2) And (D-3) up to a specific number of times; and (D-5) adding the angle parameters of all the records to calculate the second angle. The coordinate conversion method according to claim 1, wherein the step (E) comprises the following substep: (E-1) the acceleration vector is oriented in the direction of the first coordinate axis centering on the third coordinate axis Rotate an angle and record an angle parameter related to the angle; (E-2) determine whether the acceleration vector corresponds to whether the components of the first coordinate axis and the second coordinate axis are the same as before the rotation, and if yes, perform the step (E- 5), if not, performing step (E-3); (E-3) rotating the acceleration vector by an angle toward the first coordinate axis about the third coordinate axis, the tan value of the angle is Half of the tan value of the secondary rotation angle, and record an angle parameter related to the angle; (E-4) repeat steps (E-2) and (E-3) for a specific number of times; and (E-5) A quantization factor is multiplied by a component on the first coordinate axis to calculate a component length of the rotated acceleration vector projected on the first coordinate axis. The coordinate conversion method according to claim 1 or 6, wherein the step (F) comprises the following substeps: (F-1) rotating the acceleration vector about an angle of the second coordinate axis on a plane formed by the first coordinate axis and the third coordinate axis toward the first coordinate axis, and recording an angle related to the angle (F-2) determines whether the acceleration vector corresponds to the component of the third coordinate axis is zero, and if so, performs step (F-5), and if not, performs step (F-3); (F- 3) rotating the acceleration vector to an angle close to the first coordinate axis centering on the second coordinate axis, the tan value of the angle is half of the tan value of the previous rotation angle, and recording an angle related to the angle (F-4) Repeat steps (F-2) and (F-3) for a specific number of times; and (F-5) calculate the third angle by adding all the recorded angle parameters. An acceleration sensing system includes: a sensing unit configured to generate an acceleration vector according to its own motion, the acceleration vector is presented by a right angle coordinate system, and the orthogonal coordinate system is perpendicular to each other a vector axis, a second coordinate axis, and a third coordinate axis; a vector rotation unit coupled to the sensing unit; and a computing unit coupled to the vector rotation unit; the vector rotation unit first the acceleration vector Rotating around the first coordinate axis, the component of the acceleration vector projected on the plane formed by the second coordinate axis and the third coordinate axis is overlapped with the second coordinate An axis, and the calculating unit calculates a component length of the acceleration vector projected on the second coordinate axis, and the vector rotation unit centers the rotated acceleration vector on the third coordinate axis, the first coordinate axis and the second Rotating in a plane formed by the coordinate axis, the acceleration vector is superimposed on the second coordinate axis, and the calculating unit calculates the rotation vector to rotate to an angle overlapping the second coordinate axis to obtain one of the acceleration vector and the first coordinate axis a first angle; the vector rotation unit further rotates the acceleration vector around the second coordinate axis such that a component of the acceleration vector projected on a plane formed by the first coordinate axis and the third coordinate axis overlaps the third coordinate axis And the calculating unit calculates a component length of the acceleration vector projected on the third coordinate axis, and the vector rotation unit centers the rotated acceleration vector on the first coordinate axis, the second coordinate axis and the third coordinate axis Rotating on the formed plane such that the acceleration vector is superimposed on the third coordinate axis, and the calculation Converting the acceleration vector to an angle overlapping the third coordinate axis to obtain a second angle between a plane perpendicular to the acceleration vector and the second coordinate axis; the vector rotation unit further uses the acceleration vector as the third coordinate axis For center rotation, a component of the acceleration vector projected on a plane formed by the first coordinate axis and the second coordinate axis is superposed on the first coordinate axis, and the calculation unit calculates a component of the acceleration vector projected on the first coordinate axis a length, the vector rotation unit rotates the rotated acceleration vector on the second coordinate axis and rotates on a plane formed by the first coordinate axis and the third coordinate axis to overlap the acceleration vector The first coordinate axis, and the calculation unit calculates the rotation vector to rotate to an angle overlapping the first coordinate axis to obtain a third angle between a plane perpendicular to the acceleration vector and the third coordinate axis. The acceleration sensing system of claim 8, further comprising an angle adjusting unit coupled to the calculating unit, wherein the angle adjusting unit is configured to adjust according to the acceleration vector position in a quadrant area in the rectangular coordinate system The first angle is such that the angular range of the first angle satisfies the independent coordinate system. The acceleration sensing system of claim 9, wherein the vector rotation unit further subtracts the acceleration vector from the third coordinate axis by an angle of π/2 to the angle of the second coordinate axis. The first angle. A polar coordinate calculation method is performed by an electronic device, and a polar coordinate system is calculated by a vector located in a plane rectangular coordinate system. The planar rectangular coordinate system includes a first coordinate axis and a second coordinate axis, and the vector corresponds to The first target axis and the second coordinate axis form a first component and a second component, and the calculation method comprises the following steps: (A) rotating the vector by an angle in a direction close to the first coordinate axis, and recording an angle The relevant angle parameter; (B) determining whether the first component and the second component of the vector are the same as before the rotation, if yes, performing step (E), and if not, determining whether the second component is zero, and if so, stopping Following the recording of all rotation angle parameters; (C) rotating the vector in a direction close to the first coordinate axis Degree, and the tan value of the angle is half of the tan value of the previous rotation angle, and records an angle parameter related to the angle; (D) repeating steps (B) and (C) for a specific number of times; E) Add the angular parameters of all the records to obtain the angle between the vector and the first coordinate axis. According to the calculation method of the polar coordinates described in claim 11 of the patent application, the method further includes a step (F) after the step (E), and calculating the vector according to the component of the first coordinate axis in the step (E) length. According to the calculation method of the polar coordinates described in claim 12, wherein the step (F) is to multiply the component of the first coordinate axis in the step (E) by a quantization factor to calculate the original of the vector. length.