KR101806843B1 - Method for calculating arctangent, recording medium and device for performing the method - Google Patents

Abstract

The arc tangent calculation method according to the present invention includes: receiving an x-axis voltage value and a y-axis voltage value generated from a biaxial hall sensor; Converting the x-axis voltage value and the y-axis voltage value into digital data of an x-axis value and a y-axis value through an analog-to-digital converter (ADC); Simplifying an address value of a look-up table (LUT) based on an x-axis value converted into the digital data; Deriving an angle mapped to the address value from a look-up table representing 0 degrees to 90 degrees; And determining the quadrant of the first to fourth quadrants based on the sign of the x-axis value and the y-axis value. Thus, by mapping the arc tangent in the LUT without complicated calculation for a predefined section, arctangent calculations of 0 to 360 degrees can be performed with a very small-sized LUT.

Description

BACKGROUND OF THE INVENTION 1. Field of the Invention [0001] The present invention relates to an arc tangent calculation method, a recording medium and a device for performing the arc tangent calculation method,

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an arc tangent calculation method, a recording medium and an apparatus for performing the arc tangent calculation method, and more particularly, to a technique for measuring an angle using position information of a hall sensor used in a vehicle,

Hall sensors used in vehicles, mobile phones, etc. measure angles using position information. To convert the distance to an angle on such a system, the arc tangent must be calculated.

The Hall sensor is a sensor element that converts a magnetic field to a voltage difference using a Hall effect. These hall sensors measure angles, positions, speeds, etc. in various applications such as joysticks, camera lenses, automobile motors, etc., together with magnets that generate a magnetic field.

To measure the angle, the output of the 3-axis Hall sensor should be measured by measuring the distance between the X, Y, and Z axes in a rectangular coordinate system using an integrated circuit (IC) with an MCU (Micro Controller Unit). To calculate the angle, you must use the arc tan (ATAN) function.

However, since there is no divider or Floating-Point Multiplier Unit (FMU) in a low-cost microcontroller architecture, it is necessary to add complex hardware or consume a lot of computation cycles to use this function.

Specifically, KR 10-0912509 B1 proposes an inverse tangent calculation method and apparatus, but since arctangent is mapped in the LUT after calculation using the number of significant bits to simplify the LUT, complex arithmetic algorithms are required and calculation time is long do.

KR 10-1114785 B1 also presents an arctangent calculator and a computer-readable recording medium, but since arctangent mapping is performed in the LUT after a vector rotation of 45 degrees to an angle of 22.5 degrees or more in order to simplify the LUT, addition of hardware is required .

In addition, "F. Dinechin and M. Istoan," Hardware Implementations of Fixed-Point Atan2 ", in Proc. Of IEEE Symposium on Computer Arithmetic, 2015, pp. 34-41. And the error is reduced by linear interpolation of the output (see FIG. 1). However, in this case, a large LUT size is required to reduce the angular error.

KR 10-0912509 B1 KR 10-1114785 B1

 F. Dinechin and M. Istoan, "Hardware Implementations of Fixed-Point Atan2 ", in Proc. of IEEE Symposium on Computer Arithmetic, 2015, pp. 34-41.

Accordingly, it is an object of the present invention to provide an arc tangent calculation method that reduces hardware complexity.

It is another object of the present invention to provide a recording medium on which a computer program for performing an arc tangent calculation method that reduces the complexity of the hardware is recorded.

It is still another object of the present invention to provide an apparatus for performing an arc tangent calculation method that reduces the complexity of the hardware.

According to another aspect of the present invention, there is provided an arc tangent calculation method comprising: receiving an x-axis voltage value and a y-axis voltage value generated from a biaxial hall sensor; Converting the x-axis voltage value and the y-axis voltage value into digital data of an x-axis value and a y-axis value through an analog-to-digital converter (ADC); Simplifying an address value of a look-up table (LUT) based on an x-axis value converted into the digital data; Deriving an angle mapped to the address value from a look-up table representing 0 degrees to 90 degrees; And determining the quadrant of the first to fourth quadrants based on the sign of the x-axis value and the y-axis value.

In an embodiment of the present invention, the step of simplifying an address value of a look-up table (LUT) based on an x-axis value converted into the digital data may include the steps of: The approximated address value can be used as the address value of a look-up table (LUT).

In the embodiment of the present invention, the step of simplifying the address value of the look-up table (LUT) based on the x-axis value converted into the digital data may include the steps of: The x-axis value may be used as an address value of a look-up table (LUT).

In an embodiment of the present invention, the threshold may be defined such that an arc tangent calculation error is included within a certain range.

In an embodiment of the present invention, the calculation error may be 1 and the threshold value of the x-axis value may be 852. [

In the embodiment of the present invention, the x-axis value has a value from 0 to 1023, and the look-up table (LUT) can store angle data corresponding to 279 x-axis values.

According to another embodiment of the present invention, a computer program for performing the arctangent calculation method is recorded in a computer-readable storage medium.

According to another aspect of the present invention, there is provided an arctangent calculation apparatus comprising: a receiver for receiving x and y axis voltage values generated from a biaxial Hall sensor; A conversion unit for converting the x-axis and y-axis voltage values into digital data of an x-axis value and a y-axis value through an analog-digital converter (ADC); Based on the x-axis value converted into the digital data, simplifies an address value of a look-up table (LUT), and based on the x-axis value and the sign of the y- An angle calculation unit for determining a quadrant corresponding to an angle to be mapped; And a look-up table representing 0 to 90 degrees corresponding to the x-axis value and returning an angle corresponding to the address value to the angle calculation unit.

In an embodiment of the present invention, when the angle is large, the angle calculator approximates the x-axis value to use as an address value of a look-up table (LUT) The axis value can be used as the address value of the look-up table (LUT).

In the embodiment of the present invention, the analog-to-digital converter converts the data into 11-bit digital data, and the look-up table (LUT) may implement a 10-bit value.

According to the arc tangent calculation method, an ATAN function using a look-up table (LUT) is implemented to estimate angles without complicated hardware addition or long computation time. Also, to minimize the LUT, it is possible to approximate the address value in the algorithm and implement an angle measurement system with a fast computation time while reducing hardware complexity. The system implemented in accordance with the present invention can measure angles between 0 and 360 degrees and has simulated simulations with less than 1 degree error.

FIG. 1 is a conceptual diagram showing a conventional arc tangent calculation process.
2 is a block diagram of an arctangent calculation apparatus according to an embodiment of the present invention.
3 is a conceptual diagram of an angle estimation system according to the present invention.
4 is an example of an algorithm performed to estimate an angle in the MCU of FIG.
5 is an implementation example of the LUT of FIG.
6 is a graph showing simulation results for angle measurement.
7 is an enlarged view of a part of FIG.
8 is a graph showing the error value between the actual angle and the measured angle.
9 is a graph showing the characteristics of the arc tangent.
10 is a flowchart of an arc tangent calculation method according to an embodiment of the present invention.

The following detailed description of the invention refers to the accompanying drawings, which illustrate, by way of illustration, specific embodiments in which the invention may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention. It should be understood that the various embodiments of the present invention are different, but need not be mutually exclusive. For example, certain features, structures, and characteristics described herein may be implemented in other embodiments without departing from the spirit and scope of the invention in connection with an embodiment. It is also to be understood that the position or arrangement of the individual components within each disclosed embodiment may be varied without departing from the spirit and scope of the invention. The following detailed description is, therefore, not to be taken in a limiting sense, and the scope of the present invention is to be limited only by the appended claims, along with the full scope of equivalents to which such claims are entitled, if properly explained. In the drawings, like reference numerals refer to the same or similar functions throughout the several views.

Hereinafter, preferred embodiments of the present invention will be described in more detail with reference to the drawings.

2 is a block diagram of an arctangent calculation apparatus according to an embodiment of the present invention. 3 is a conceptual diagram of an angle estimation system according to the present invention.

The arctangent calculation apparatus 10 (hereinafter, referred to as a device) according to the present invention predefines an LUT interval through error analysis to minimize the size of a look-up table (LUT) .

This method implements an angle measuring system 1 that reduces hardware complexity, and the system 1 of the present invention can calculate an arc tangent with an error of less than one degree from an angle between 0 and 360 degrees.

The arctangent is the inverse of the tangent function, sometimes referred to as the inverse tangent function, and is represented by arctan or tan ^{- 1} .

2 and 3, the apparatus 10 according to the present invention includes a hall sensor 110, a conversion unit 130, an angle calculation unit 150, and an LUT 170. [

The apparatus 10 of the present invention may be implemented with software (application) for performing arc tangent calculation and the Hall sensor 110, the conversion unit 130, the angle calculation unit 150, The configuration of the LUT 170 may be controlled by software for performing the arc tangent computation performed in the apparatus 10. [

The device 10 may be a separate terminal or some module of the terminal. The configuration of the hall sensor 110, the conversion unit 130, the angle calculation unit 150, and the LUT 170 may be an integrated module or may be composed of one or more modules. However, conversely, each configuration may be a separate module.

The device 10 may be mobile or stationary. The device 10 may be in the form of a server or an engine and may be a device, an apparatus, a terminal, a user equipment (UE), a mobile station (MS) a wireless device, a handheld device, and the like.

The device 10 may execute or produce various software based on an operating system (OS), i.e., a system. The operating system is a system program for allowing software to use the hardware of a device. The operating system includes a mobile computer operating system such as Android OS, iOS, Windows Mobile OS, Sea OS, Symbian OS, Blackberry OS, MAC, AIX, and HP-UX.

The hall sensor 110 detects a direction and a size of a magnetic field by using a Hall effect in which a voltage is generated in a direction perpendicular to a current and a magnetic field when a magnetic field is applied to a conductor through which current flows. At this time, the generated voltage is proportional to the intensity of the current and the magnetic field, and when the current is constant, an output proportional to the intensity of the magnetic field is generated.

The Hall sensor 110 according to an embodiment of the present invention may be a two-axis Hall sensor having values of x axis and y axis. The hall sensor 110 outputs the x-axis voltage value and the y-axis voltage value to the conversion unit 130.

The conversion unit 130 converts the x-axis voltage value and the y-axis voltage value received from the hall sensor 110 into an x-axis value and a y-axis value through an analog-to-digital converter (ADC) Data.

In one embodiment, the conversion unit 130 converts the x-axis voltage value and the y-axis voltage value into digital data through an 11-bit analog-to-digital converter (ADC) And transmits it to the unit 150.

In the environment where the center axes of the magnetic fields generated by the hall sensor and the magnet coincide with each other and the offset voltage and sensitivity of the hall sensor are corrected as shown in the following equations (1) and (2), the square of the x- The square has a constant value. Therefore, the angle can be found in the LUT through the x-axis value.

[Equation 1]

&Quot; (2) "

The angle calculator 150 simplifies an address value of a look-up table (LUT) based on the x-axis value converted into the digital data, and derives an angle mapped to the address value. Further, based on the sign of the x-axis value and the y-axis value, a quadrant corresponding to the angle is determined to calculate the final arc tangent.

Since the arctangent value is nonlinear with respect to the linear x-axis value, when the angle is large, the x-axis value is approximated to be used as an address value of the LUT. When the angle is small, Can be used as an address value.

The angle calculation unit 150 may be implemented in an MCU (Micro Controller Unit) such as a vehicle or a mobile phone, and the LUT 170 may be implemented in an internal memory or a separate memory.

Referring to FIG. 4, an example of an algorithm performed to estimate an angle implemented in the MCU is shown. In the present invention, arctangent is mapped in the LUT 170 without a complicated calculation process for a predefined section.

To do this, we predefine the LUT interval through error analysis and approximate the address value in the algorithm. The defined interval may be defined as a section defining an arc tangent calculation error within a certain range.

For example, when the x-axis value is less than the threshold value, the approximated address value is used, and when the x-axis value is equal to or greater than the threshold value, the x-axis value can be used as the address value. The threshold may be an x-axis value of 852.

FIG. 6 is a graph showing simulation results for angle measurement, and FIG. 7 is an enlarged view of part of FIG. 8 is a graph showing the error value between the actual angle and the measured angle.

Referring to FIG. 8, since the x-axis value is 852 or more and the calculation error is 1 degree or more, the approximated address value LUT can be used when the x-axis value is less than 852 for less than 1 degree error. Therefore, an error caused by rounding with integer data when the number is 852 or more, and an error due to an approximated address value occurs when the number is less than 852.

Also, the angle calculator 150 can know the quadrant of the x-axis value and the y-axis value. That is, one of the first to fourth quadrants corresponds to the following algorithm.

First quadrant: x> 0, y> 0, Angle = LUT [x]

Fourth quadrant: x> 0, y <0, Angle = 360 - LUT [x]

Second quadrant: x <0, y> 0, Angle = 180 - LUT [x]

Third quadrant: x <0, y <0, Angle = 180 + LUT [x]

Therefore, even if the LUT implements only a value corresponding to 10 bits corresponding to half of the ADC resolution, the angle value can be expressed as a value between 0 and 360 degrees.

At this time, arctangent values for the linear x-axis values are nonlinear, so having a LUT for all x-axis values leads to a waste of hardware area. Accordingly, when the angle is large, the x-axis value is approximated to be used as the address value of the LUT. When the angle is small, the x-axis value is directly used as the address value.

Therefore, it is not necessary to provide all the memories for the x-axis values from 0 to 1023. Since the MCU has only a 16-bit fixed point calculator, the LUT has 16-bit integer data scaled 512 times.

The LUT 170 can further simplify the 1024 x-axis values and calculate arctangent with an error of less than 1 with only 279 LUTs. Referring to FIG. 5, there is shown a LUT storing an angle mapping to an x-axis value.

The LUT 170 according to the present invention represents 0 to 90 degrees, and other angles can be processed on the algorithm performed by the angle calculator 150. [

Because the x-axis and y-axis values indicate the quadrant, the LUT has a value between 0 and 360 degrees even if only the 10 bits corresponding to half the resolution of the ADC are implemented. . Accordingly, the LUT 170 according to the present invention can be reduced very small.

This is because, as shown in Fig. 9, the arc tangent angle is repeated. The arc tangent values in Fig. 9 are as follows.

Accordingly, the present invention requires only 1/4 of the conventional look-up table, thereby greatly reducing the size of the LUT. It is suitable for application to electronic apparatuses that are further downsized and compacted in accordance with the reduction of the size of the LUT.

The present invention proposes a low-cost system for measuring the angle from the position information of the hall sensor. The present invention implements an arc tangent (ATAN) function using an LUT to estimate angles without adding complex hardware or long computation time.

In order to miniaturize the LUT, the address value is approximated according to the error value, and the implemented function has an error of less than 1 degree from 0 to 360 degrees in the simulated simulation environment, so that a very accurate result can be obtained.

10 is a flowchart of an arc tangent calculation method according to an embodiment of the present invention.

The arctangent calculation method according to the present embodiment can be carried out in substantially the same configuration as the apparatus 10 of Fig. Therefore, the same components as those of the device 10 of FIG. 2 are denoted by the same reference numerals, and repeated descriptions are omitted. Further, the arc tangent calculation method according to the present embodiment can be executed by software (application) for performing arc tangent calculation.

Referring to FIG. 10, the arc tangent calculation method according to the present embodiment receives an x-axis voltage value and a y-axis voltage value generated from a biaxial hall sensor (step S10).

The Hall sensor detects a direction and a size of a magnetic field by using a Hall effect in which a voltage is generated in a direction perpendicular to a current and a magnetic field when a magnetic field is applied to a conductor through which current flows. At this time, the generated voltage is proportional to the intensity of the current and the magnetic field, and when the current is constant, an output proportional to the intensity of the magnetic field is generated.

The Hall sensor according to an embodiment of the present invention may be a two-axis hall sensor having values of x axis and y axis and outputs x axis voltage value and y axis voltage value.

The x-axis voltage value and the y-axis voltage value are converted into digital data of an x-axis value and a y-axis value through an analog-to-digital converter (ADC) (step S30).

In a circumstance where the center axes of the magnetic field generated by the Hall sensor and the magnet coincide with each other and the offset voltage and sensitivity of the hall sensor are corrected, the square of the x-axis value and the square of the y-axis value are constant. Therefore, the angle can be found in the LUT through the x-axis value.

The address value of the look-up table (LUT) is simplified based on the x-axis value converted into the digital data (step S50).

In the step of simplifying the address value (step S50), since the arctangent value is nonlinear with respect to the linear x-axis value, when the angle is large, the x-axis value is approximated to be used as the address value of the LUT, In this case, the x-axis value can be directly used as the address value.

The step of simplifying the address value (step S50) may be implemented in an MCU (Micro Controller Unit) such as a vehicle or a mobile phone, and the LUT may be implemented in an internal memory or a separate memory of the MCU.

In the present invention, the LUT interval is predefined through error analysis, and the address value is approximated on the algorithm. The defined interval may be defined as a section defining an arc tangent calculation error within a certain range.

For example, when the x-axis value is less than the threshold value, the approximated address value is used, and when the x-axis value is equal to or greater than the threshold value, the x-axis value can be used as the address value. For example, if the computation error is set to less than one degree, the threshold may be an x-axis value of 852.

In this case, since the calculation error is more than 1 degree from the x-axis value of 852 or more, the approximated address value LUT can be used when the x-axis value is less than 852 for less than 1 degree error. Therefore, an error caused by rounding with integer data when the number is 852 or more, and an error due to an approximated address value occurs when the number is less than 852.

When an address value of the LUT is derived, an angle mapped to the address value is derived from a look-up table expressing 0 degrees to 90 degrees (step S70). Further, based on the sign of the x-axis value and the y-axis value, it is determined which quadrant of the first to fourth quadrants (step S90).

The LUT according to the present invention represents from 0 to 90 degrees, and other angles can be processed in an algorithm. Accordingly, the LUT according to the present invention requires only 1/4 of the conventional look-up table, and the size of the LUT can be greatly reduced.

Referring to FIG. 4, an example of an algorithm performed to estimate an angle implemented in the MCU is shown. In the present invention, the arctangent is mapped in the LUT without complicated calculation for a predefined period.

Therefore, the angle can be found in the LUT through the x-axis value. Since the x-axis value and the y-axis value indicate the quadrants, the LUT has 0 to 10 degrees even if only 10 bits corresponding to half of the ADC resolution are implemented. It can be expressed as a value between 360 degrees.

At this time, arctangent values for the linear x-axis values are nonlinear, so having a LUT for all x-axis values leads to a waste of hardware area. Accordingly, when the angle is large, the x-axis value is approximated to be used as the address value of the LUT. When the angle is small, the x-axis value is directly used as the address value.

Therefore, it is not necessary to provide all the memories for the x-axis values from 0 to 1023. Since the MCU has only a 16-bit fixed point calculator, the LUT has 16-bit integer data scaled 512 times.

Accordingly, arctangent with an error of less than one degree can be calculated even with only 279 LUTs by further simplifying the 1024 x-axis values. Further, the present invention can estimate the angle with a small-sized LUT without adding complicated hardware or a long computation time.

Such arctangent calculation methods may be implemented in an application or implemented in the form of program instructions that may be executed through various computer components and recorded on a computer-readable recording medium. The computer-readable recording medium may include program commands, data files, data structures, and the like, alone or in combination.

The program instructions recorded on the computer-readable recording medium may be ones that are specially designed and configured for the present invention and are known and available to those skilled in the art of computer software.

Examples of computer-readable recording media include magnetic media such as hard disks, floppy disks and magnetic tape, optical recording media such as CD-ROMs and DVDs, magneto-optical media such as floptical disks, media, and hardware devices specifically configured to store and execute program instructions such as ROM, RAM, flash memory, and the like.

Examples of program instructions include machine language code such as those generated by a compiler, as well as high-level language code that can be executed by a computer using an interpreter or the like. The hardware device may be configured to operate as one or more software modules for performing the processing according to the present invention, and vice versa.

It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit or scope of the present invention as defined by the following claims. You will understand.

In order to reduce the hardware complexity and the number of operation cycles, the present invention implements an ATAN function using the LUT method to reduce the size of the LUT. Accordingly, the present invention can be applied to various angular measurement systems such as a smart phone, a joystick, a camera, and a vehicle using a Hall sensor.

1: Angle estimation system
10: arctangent calculation device
110: hall sensor
130:
150:
170: LUT

Claims (10)

Receiving an x-axis voltage value and a y-axis voltage value generated from the biaxial hall sensor;
Converting the x-axis voltage value and the y-axis voltage value into digital data of an x-axis value and a y-axis value through an analog-to-digital converter (ADC);
Simplifying an address value of a look-up table (LUT) based on an x-axis value converted into the digital data;
Deriving an angle mapped to the address value from a look-up table representing 0 degrees to 90 degrees; And
Determining a quadrant of the first to fourth quadrants based on the sign of the x-axis value and the y-axis value.
The method of claim 1, wherein the step of simplifying an address value of a look-up table (LUT) based on an x-
Wherein the approximated address value is used as an address value of a look-up table (LUT) when the x-axis value is less than a threshold value.
3. The method of claim 2, wherein the step of simplifying an address value of a look-up table (LUT) based on an x-
Axis value is used as an address value of a look-up table (LUT) when the x-axis value is equal to or greater than a threshold value.
3. The method of claim 2,
Wherein the threshold defines the arc tangent calculation error to be within a certain range.
5. The method of claim 4,
Wherein the calculation error is 1 and the threshold value of the x-axis value is 852. [
The method according to claim 1,
Wherein the x-axis value has a value from 0 to 1023, and the look-up table (LUT) stores angle data corresponding to 279 x-axis values.
A computer-readable recording medium on which a computer program is recorded, for performing the arc tangent calculation method according to any one of claims 1 to 6.
A receiving unit for receiving x-axis and y-axis voltage values generated from the biaxial hall sensor;
A conversion unit for converting the x-axis and y-axis voltage values into digital data of an x-axis value and a y-axis value through an analog-digital converter (ADC);
Based on the x-axis value converted into the digital data, simplifies an address value of a look-up table (LUT), and based on the x-axis value and the sign of the y- An angle calculation unit for determining a quadrant corresponding to an angle to be mapped; And
And a look-up table which represents 0 to 90 degrees corresponding to the x-axis value and returns an angle corresponding to the address value to the angle calculation unit.
9. The apparatus according to claim 8,
If the angle is large, the x-axis value is approximated and used as an address value of a look-up table (LUT). If the angle is small, the x-axis value is referred to as a look-up table ; LUT). &Lt; / RTI &gt;
9. The method of claim 8,
Wherein the analog-to-digital converter converts the digital data into 11-bit digital data, and the look-up table (LUT) implements a 10-bit value.

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