JP6485195B2 - Inclination measuring method and apparatus, electronic apparatus and program - Google Patents

Description

  The present invention relates to an inclination measuring method and apparatus, an electronic apparatus, a program, and the like.

  The output of the acceleration sensor includes bias and drift due to environmental changes and changes with time. Further, as an error peculiar to the acceleration sensor, when the device including the acceleration sensor is inclined with respect to the horizontal plane, an error (offset) due to the gravitational acceleration component occurs in the output of the acceleration sensor.

  In Patent Document 1, acceleration detection is performed in a stationary state (acceleration = 0) before and after the acceleration sensor 10 arranged on a moving body such as a bicycle is inverted 180 ° in the horizontal direction, and an average value of both detection values is obtained. The offset amount based on the inclination is obtained.

  According to Patent Document 2, the output value of the sensitivity axis is based on the output value of the sensitivity axis when the angular position of the turntable is 0 degrees (S1), 90 degrees (S2), 180 degrees (S3), and 270 degrees (S4). A calibration value for correcting the above is obtained. Specifically, simultaneous linear equations representing two straight lines are solved from statistical average values of static data of four points (S1 to S4) with different phases of 90 degrees, and the maximum and minimum output points and amplitude of the multi-axis sensor are calculated. The calibration value is calculated by obtaining the center value.

  In Patent Document 3, in order to provide an angular velocity sensor that detects an angular velocity even when the detection surface is tilted, at least three acceleration detection units are installed in the same plane as the angular velocity detection unit. After calculating the inclination angle of the angular velocity detection surface using the acceleration detected by these acceleration detectors, the fluctuation amount of the angular velocity due to the inclination angle is estimated and corrected.

JP 2004-354214 A (0013) JP 2010-281598 A (0044-0045) Japanese Patent Laid-Open No. 06-324066

  In Patent Documents 1 and 2, the acceleration sensor is rotated to 0 ° and 180 ° stop positions (Patent Document 1), or the acceleration sensor is rotated to 0 °, 90 °, 180 °, and 270 ° stop positions. (Patent Document 2), acceleration is detected by an acceleration sensor in a stationary state at each stop position, and an offset amount and a calibration value are obtained based on an average value thereof. There is still an error in the offset amount and the calibration value obtained by such a method.

  A sensor device equipped with an acceleration sensor is installed horizontally, but the installation surface may be inclined due to an external factor such as an earthquake. Or when a sensor apparatus is mounted in a moving body like patent document 1, the moving surface inclines. In such a case, it is necessary to measure the degree of inclination (inclination angle or inclination direction) with respect to the horizontal plane. When measuring the inclination, a gravitational acceleration component due to inclination is superimposed as an error (also referred to as inclination error) on the measurement value of the acceleration sensor. Further, even when the sensor device is rotated to obtain an offset amount or a calibration value as in Patent Documents 1 and 2, a drift (also referred to as a dynamic error) that differs at each stop position before and after the rotation, or at each stop position It is necessary to remove a substantially constant bias (also referred to as static error).

  In some aspects of the present invention, the error superimposed on the output of the acceleration sensor is different drift (dynamic error) at each stop position before and after the rotation, and a substantially constant bias (static) at each stop position. An object of the present invention is to provide an inclination measuring method and apparatus, an electronic device, and a program that can accurately measure the inclination (inclination angle and inclination azimuth) of the installation surface of the acceleration sensor by removing an error.

(1) According to one aspect of the present invention, there is provided a first measurement orientation in which one of the orthogonal two-axis detection axes of an acceleration sensor having an orthogonal two-axis detection axis on a virtual plane intersecting the gravity direction is set as a reference orientation. , In a stationary state set to each of the second measurement azimuth 180 degrees away from the first measurement azimuth at the rotational position around the normal to the virtual plane and the third measurement azimuth returned to the reference azimuth. An error measurement step of measuring a different dynamic error in each of the first to third measurement orientations using an output of an acceleration sensor having the detection axes of the two orthogonal axes measured by
The dynamic error and the substantially constant static error in each of the first to third measurement directions are removed from the output of the acceleration sensor set to the first measurement direction and the second measurement direction. An inclination measuring step for measuring at least one of the inclination angle and the inclination azimuth based on the data depending on the inclination angle and the inclination azimuth angle with which the virtual plane is inclined with respect to the horizontal plane;
Have
The error measurement step relates to an inclination measurement method including a step of measuring the dynamic error based on a difference between outputs of the acceleration sensors set in the first measurement direction and the third measurement direction.

  The first measurement direction and the third measurement direction are parallel to the same direction in which the detection axes of the acceleration sensor are both set as the reference direction. Here, the output of the acceleration sensor measured in a stationary state includes a dynamic error (drift) inherent to the measurement direction, a static error (bias) that is equal in other measurement directions, and a characteristic inherent to the measurement direction. A tilt error is included (see equations (7) and (8) below). Further, as shown in equations (7) and (8) described later, since the tilt error depends on the tilt angle φ and the tilt direction θ, the unknown is 4. Therefore, the detection axis is set to a total of three or more different measurement directions, and the measurement is performed a total of four times or more (measurement is performed twice in the reference direction on one of the two orthogonal detection axes). In the case of an acceleration sensor having two orthogonal detection axes, a total of four or more measurement orientations (0 °, 90 °) can be obtained by setting each of the orthogonal two axes as the second measurement orientation and then returning it to the reference orientation. (°, 180 °, 270 °, 360 ° = 0 °).

  Here, the difference in the output of the acceleration sensor in the first and third measurement directions which are the same parallel direction is the difference in dynamic error between the first measurement direction and the third measurement direction. The difference in the dynamic error may be tilt change during measurement, temperature characteristic fluctuation, environmental vibration change, random drift, etc., but the measurement itself is performed in a relatively short time, and the measurement timing is also small in environmental temperature fluctuation. By selecting a stable time zone and making the current consumption change of the measuring terminal stable at the time of measurement, it is possible to reduce the inclination change or the environmental vibration change during the measurement so that it can be almost ignored. In addition, by appropriately selecting the measurement conditions, the random drift can be reduced so that it can be almost ignored. Therefore, for example, the dynamic error of the first measurement azimuth is zero, the dynamic error is the maximum or the minimum in the third measurement azimuth, and the dynamic error of the second measurement azimuth between the third measurement azimuth and the first measurement azimuth. Can be assigned based on the difference in dynamic error between the first and third measurement orientations.

  If random drift is ignored, the output of the acceleration sensor in a stationary state is a tilt error (depending on tilt angle φ and tilt direction θ), dynamic error and static error due to the gravitational acceleration component due to the tilt of the virtual plane with respect to the horizontal plane. It is the total sum of errors. By removing the dynamic error and the static error from the output of the acceleration sensor in the stationary state, the tilt error is obtained, and at least one of the tilt angle and the tilt azimuth angle can be measured from the tilt error.

(2) In one aspect of the present invention, in the inclination measuring step, the two orthogonal detection axes are the X axis and the Y axis, the inclination angle is φ, the inclination azimuth is θ, and the virtual plane When the gravity component projected onto Iφ is Iφ, the X-axis component X ″ ₀ = Iφ (cosθ) and the Y-axis component Y ″ ₀ = Iφ (sinθ) of the gravity in the first measurement direction, X-axis component X ″ ₁ = −X ″ ₀ and Y-component Y ″ ₁ = −Y ″ ₀ of gravity in the orientation, and the X-axis component of gravity in the first measurement orientation and the second measurement orientation Average value X ″ ₀₁ = (X ″ ₀ −X ″ ₁ ) / 2, and the average value Y ″ ₀₁ = (Y ″ _{0) of the} Y-axis component of gravity in the first measurement direction and the second measurement direction _"using the ^{_{1) / 2, Iφ = (}} X" -Y 01 2 + Y "01 2) seeking ^1/2, is possible to calculate a tilt angle φ = 180 × Iφ / π Kill.

In this way, since the first and second measurement orientations are in the same direction and in the opposite direction, using the relationship of X ″ ₁ = −X ″ ₀ and Y component Y ″ ₁ = −Y ″ ₀ , The inclination angle φ can be determined relatively easily.

(3) In one aspect of the present invention, in the inclination measuring step, the orthogonal biaxial detection axes are the X axis and the Y axis, the inclination angle is φ, the inclination azimuth is θ, and the virtual plane When the gravity component projected onto Iφ is Iφ, the X-axis component X ″ ₀ = Iφ (cosθ) and the Y-axis component Y ″ ₀ = Iφ (sinθ) of the gravity in the first measurement direction, X-axis component X ″ ₁ = −X ″ ₀ and Y component Y ″ ₁ = −Y ″ ₀ of gravity in the azimuth, X-axis component X ″ ₁ = −X ″ ₀ and Y in the second measurement direction The component Y ″ ₁ = −Y ″ ₀ is obtained, and the average value X ″ ₀₁ = (X ″ ₀ −X ″ ₁ ) / of the X-axis component of gravity in the first measurement orientation and the second measurement orientation Iø = with 2, the average value _{Y "01 = (Y" 0} -Y "1) / 2 of the Y-axis component of gravity in the first measuring direction and the second measuring orientation ( ^{_{"01 2 + Y" 01 2}} ) seeking ^1/2, said X and Y-axis component _{X "0, X" 1,} Y "0, Y" 1 was normalized by dividing Iø, the tilt azimuth angle θ Can be measured.

Also in this case, since the first and second measurement orientations are in the same direction and in the opposite direction, the relationship of X ″ ₁ = −X ″ ₀ and the Y component Y ″ ₁ = −Y ″ ₀ is used, The tilt azimuth angle θ can be obtained relatively easily.

(4) According to another aspect of the present invention, a first measurement orientation in which one of the orthogonal biaxial detection axes of an acceleration sensor having an orthogonal biaxial detection axis on a virtual plane intersecting the direction of gravity is set as a reference orientation. A second measurement orientation 90 degrees away from the first measurement orientation at a rotational position around the normal to the virtual plane, and 180 degrees away from the first measurement orientation at a rotational position around the normal. The third measurement azimuth, the fourth measurement azimuth 270 degrees away from the first measurement azimuth at the rotational position around the normal line, and the fifth measurement azimuth returned to the reference azimuth and the stationary state An error measurement step of measuring a different dynamic error in each of the first to fifth measurement orientations using an output of the detection axes of the two orthogonal axes of the acceleration sensor measured in
The dynamic error and the substantially constant static error in each of the first to fifth measurement directions are removed from the output of the acceleration sensor set to the first to fourth measurement directions, An inclination measurement step for measuring at least one of the inclination angle and the inclination azimuth based on data depending on an inclination angle and an inclination azimuth angle at which the virtual plane is inclined with respect to a horizontal plane;
Have
The error measurement step relates to an inclination measurement method including a step of measuring the dynamic error based on a difference between outputs of the acceleration sensors set in the first measurement direction and the fifth measurement direction.

  Another aspect of the present invention is a two-axis four-direction rotation measurement, which is different from the two-axis two-direction rotation measurement which is one aspect of the present invention, and each of the orthogonal two-axis detection axes is set to four different measurement directions. Thus, at least one of the tilt angle and the tilt azimuth angle can be measured.

(5) In another aspect of the present invention, in the inclination measuring step, the orthogonal biaxial detection axes are an X axis and a Y axis, the inclination angle is φ, the inclination azimuth is θ, and the virtual When the gravity component projected onto the plane is Iφ, the X-axis component X ″ ₀ = Iφ (cos θ) and the Y-axis component Y ″ ₀ = Iφ (sin θ) of the gravity in the first measurement direction, X-axis component X ₁ = Iφ (sin θ) and Y component Y ₁ = Iφ (cos θ) of gravity in the measurement direction, and X component X ″ ₂ = −X ″ ₀ and Y component of gravity in the third measurement direction Y ″ ₂ = −Y ″ ₀ and the X-axis component X ″ ₃ = −X ″ ₁ and the Y component Y ″ ₃ = −Y ″ ₁ of gravity in the fourth measurement orientation, and the first measurement orientation mean and of the X-axis component of gravity in the third measuring azimuth value _{X "03 = (X" 0} -X "3) / 2 or the average of the Y-axis component value _{Y" 03} = And _{Y "0 -Y" 3) /} 2, the average value _{X "24 = (X" 2} -X "4 of said X-axis component of gravity in the second measurement direction and the fourth measuring azimuth) / 2 or Using the average value Y ″ ₂₄ = (Y ″ ₂ −Y ″ ₄ ) / 2 of the Y-axis component, Iφ = (X ″ ₀₃ ² + X ″ ₂₄ ² ) ^1/2 or Iφ = (Y ″ ₀₃ ² + Y ″ ₂₄ ² ) ^1/2 is obtained, and the inclination angle φ = 180 × Iφ / π can be calculated.

In this case, since the first and third measurement directions are in the same direction and in the reverse direction, and the second and fourth measurement directions are in the same direction and in the reverse direction, X ″ ₂ = −X ″ ₀ , Using the relationship of X ″ ₃ = −X ″ ₁ and Y component Y ″ ₂ = −Y ″ ₀ , Y ″ ₃ = −Y ″ ₁ , the tilt angle φ can be determined relatively easily.

(6) In another aspect of the present invention, in the inclination measuring step, the detection axes of the two orthogonal axes are the X axis and the Y axis, the inclination angle is φ, the inclination azimuth is θ, and the virtual When the gravity component projected onto the plane is Iφ, the X-axis component X ″ ₀ = Iφ (cos θ) and the Y-axis component Y ″ ₀ = Iφ (sin θ) of the gravity in the first measurement direction, X-axis component X ₁ = Iφ (sin θ) and Y component Y ₁ = Iφ (cos θ) of gravity in the measurement direction, and X component X ″ ₂ = −X ″ ₀ and Y component of gravity in the third measurement direction Y ″ ₂ = −Y ″ ₀ and the X-axis component X ″ ₃ = −X ″ ₁ and the Y component Y ″ ₃ = −Y ″ ₁ of gravity in the fourth measurement orientation, and the first measurement orientation mean and of the X-axis component of gravity in the third measuring azimuth value _{X "03 = (X" 0} -X "3) / 2 or the average of the Y-axis component value _{Y" 03} = And _{Y "0 -Y" 3) /} 2, the average value _{X "24 = (X" 2} -X "4 of said X-axis component of gravity in the second measurement direction and the fourth measuring azimuth) / 2 or Using the average value Y ″ ₂₄ = (Y ″ ₂ −Y ″ ₄ ) / 2 of the Y-axis component, Iφ = (X ″ ₀₃ ² + X ″ ₂₄ ² ) ^1/2 or Iφ = (Y ″ ₀₃ ² + Y ″ ₂₄ ² ) ^1/2 is obtained, the X and Y axis components X ″ ₀ , X ″ ₁ , Y ″ ₀ , Y ″ ₁ are divided by Iφ and normalized to measure the tilt azimuth angle θ. be able to.

In this case, since the first and third measurement directions are in the same direction and in the reverse direction, and the second and fourth measurement directions are in the same direction and in the reverse direction, X ″ ₂ = −X ″ ₀ , By using the relationship of X ″ ₃ = −X ″ ₁ and Y component Y ″ ₂ = −Y ″ ₀ , Y ″ ₃ = −Y ″ ₁ , the tilt azimuth angle θ can be obtained relatively easily.

(7) In the above aspect (3) or (6), the gradient measuring step is performed by dividing the X and Y axis components X ″ ₀ , X ″ ₁ , Y ″ ₀ , Y ″ ₁ by Iφ. The normalized X and Y axis components X ′ ″ ₀ , X ′ ″ ₁ , Y ′ ″ ₀ , Y ″ ′ ₁ having an amplitude of ± 1 are converted into orthogonal coordinates on a Gaussian plane, and the tilt direction A step of determining in which of the first to fourth quadrants of the Gaussian plane the angle θ exists may be included. This is because the coincidence and non-coincidence of the tilt azimuth obtained by the complex number of the real number and the imaginary number are related to the quadrant where the tilt azimuth exists.

  (8) In one aspect of the present invention, when the measurement in the first to third measurement orientations is one cycle, when the cycle number n is 2 or more, the measurement is performed over n cycles, and the nth cycle The first measurement direction can also be used as the measurement direction of the (n-1) th cycle.

  By sampling the measurement values over n cycles in this way, the measurement accuracy can be increased and the same measurement values can be used in two adjacent cycles.

  Further, in one aspect of the present invention, the main measurement is performed in a stationary state while continuously changing the azimuth, and the measurement is measured at approximately equal time intervals in the order of measurement, and continuously rotated while changing the azimuth. A section of one cycle can be extracted from the measurement data string when measured and analyzed. In this extracted one-cycle section, the first and last azimuths of the cycle are the same, and the other azimuths are sections including all the azimuths necessary for measurement. This measurement order has priority over the order of orientation, and the orientation need not be in order of measurement.

  In one embodiment of the present invention, dynamic errors are measured in the order of measurement in one extracted cycle, and an average value is obtained for data in the same direction in the data in one cycle for a data string in which dynamic errors have been corrected. Thus, it is possible to generate data rounded for each measurement direction and proceed to a procedure for measuring the static error for this result.

  In one aspect of the present invention, the reference direction of the measurement direction of rotation measurement is related to the North-East-Down (NED) coordinate system of the environment where the sensor is installed, and the direction is determined and installed. The resulting tilt azimuth can be indicated by the environmental coordinate system orientation.

  (9) In one aspect of the present invention, the detection axis of the acceleration sensor is rotated in the first direction from the reference azimuth, and then the second direction opposite to the first direction toward the reference azimuth. It may be rotated in the direction. In this way, the dynamic error bias is averaged.

(10) Still another aspect of the present invention provides:
One of the orthogonal biaxial detection axes of the acceleration sensor having an orthogonal biaxial detection axis in a virtual plane that intersects the direction of gravity is set to a first measurement direction set as a reference direction, and around a normal to the virtual plane Means for outputting a command to set each of the second measurement azimuth 180 degrees away from the first measurement azimuth at the rotational position and the third measurement azimuth returned to the reference azimuth;
Means for receiving an output of the acceleration sensor set in each of the first to third measurement directions;
Error measurement means for measuring different dynamic errors in each of the first to third measurement orientations using the output of the acceleration sensor;
From the output of the acceleration sensor set to the measurement direction of each of the first measurement direction and the second measurement direction, the dynamic error is substantially constant in each of the first to third measurement directions. Means for measuring at least one of the tilt angle and the tilt azimuth angle based on data depending on a tilt angle and a tilt azimuth angle at which the virtual plane is tilted with respect to a horizontal plane, from which static errors have been removed;
Have
The error measuring unit relates to a tilt measuring device that measures the dynamic error based on a difference between outputs of the acceleration sensor set in the first measurement direction and the third measurement direction.
About.

  With the inclination measuring device according to still another aspect of the present invention, the slope measuring method according to one aspect of the present invention can be suitably implemented.

(11) Still another aspect of the present invention provides:
One of the orthogonal biaxial detection axes of the acceleration sensor having an orthogonal biaxial detection axis in a virtual plane that intersects the direction of gravity is set to a first measurement direction set as a reference direction, and around a normal to the virtual plane A second measurement orientation 90 degrees away from the first measurement orientation at a rotational position, a third measurement orientation 180 degrees away from the first measurement orientation at a rotational position around the normal, and the normal Means for outputting a command to be set for each of a fourth measurement azimuth 270 degrees away from the first measurement azimuth at a rotational position around and a fifth measurement azimuth returned to the reference azimuth;
Means for receiving an output of the acceleration sensor set in each of the first to third measurement directions;
Error measurement means for measuring different dynamic errors in each of the first to fifth measurement orientations using the output of the acceleration sensor;
From the output of the acceleration sensor set to the measurement direction of each of the first to fourth measurement directions, the dynamic error and a static error that is substantially constant in each of the first to fifth measurement directions. Means for measuring at least one of the tilt angle and the tilt azimuth angle based on data depending on the tilt angle and tilt azimuth angle at which the virtual plane is tilted with respect to the horizontal plane.
Have
The error measuring unit relates to a tilt measuring device that measures the dynamic error based on a difference between outputs of the acceleration sensors set in the first measurement direction and the fifth measurement direction.

  The gradient measuring apparatus according to still another aspect of the present invention can suitably implement the slope measurement method according to another aspect of the present invention.

  (12) Still another aspect of the present invention defines an electronic apparatus having the error measurement device according to (8) or (9).

(13) Still another aspect of the present invention provides:
One of the orthogonal biaxial detection axes of the acceleration sensor having an orthogonal biaxial detection axis in a virtual plane that intersects the direction of gravity is set to a first measurement direction set as a reference direction, and around a normal to the virtual plane Outputting a command to set each of the second measurement azimuth 180 degrees away from the first measurement azimuth at the rotational position and the third measurement azimuth returned to the reference azimuth;
Receiving an output from the acceleration sensor set in the first to third measurement directions;
A procedure for measuring different dynamic errors in each of the first to third measurement orientations using the output of the acceleration sensor measured in a stationary state in each of the first to third measurement orientations;
From the output of the acceleration sensor set to each of the first measurement direction and the second measurement direction, the dynamic error and the static error that is substantially constant in each of the first to third measurement directions. Measuring at least one of the tilt angle and the tilt azimuth angle based on data depending on a tilt angle and a tilt azimuth angle at which the virtual plane is tilted with respect to a horizontal plane from which an error is removed;
To the computer,
The procedure for measuring the dynamic error includes a procedure for measuring the dynamic error based on a difference between outputs of the acceleration sensor in the first measurement direction and the third measurement direction. About.

(14) Still another aspect of the present invention provides:
One of the orthogonal biaxial detection axes of the acceleration sensor having an orthogonal biaxial detection axis in a virtual plane that intersects the direction of gravity is set to a first measurement direction set as a reference direction, and around a normal to the virtual plane A second measurement orientation 90 degrees away from the first measurement orientation at a rotational position; a third measurement orientation 180 degrees away from the first measurement orientation at a rotational position around a normal to the virtual plane; A procedure for outputting a command to be set for each of the fourth measurement azimuth 270 degrees away from the first measurement azimuth at the rotational position around the normal to the virtual plane and the fifth measurement azimuth returned to the reference azimuth. When,
Receiving an output from the acceleration sensor set in the first to fifth measurement directions;
A procedure for measuring different dynamic errors in each of the first to fifth measurement orientations using the output of the acceleration sensor measured in a stationary state in each of the first to fifth measurement orientations;
From the output of the acceleration sensor set to the measurement direction of each of the first to fourth measurement directions, the dynamic error and a substantially constant static error in each of the first to fifth measurement directions Measuring at least one of the tilt angle and the tilt azimuth angle based on data depending on the tilt angle and tilt azimuth angle at which the virtual plane is tilted with respect to the horizontal plane,
To the computer,
The procedure for measuring the dynamic error relates to a program including a procedure for measuring the dynamic error based on a difference between outputs of the acceleration sensor in the first measurement direction and the fifth measurement direction.

  By installing these programs in a general-purpose machine such as a personal computer, it is possible to measure the inclination with the general-purpose machine.

1 is an overall view of a measurement system according to an embodiment of the present invention. It is an external view of the measurement terminal device shown in FIG. It is a perspective view which shows arrangement | positioning of the triaxial acceleration sensor arrange | positioned in the housing | casing shown in FIG. It is a figure which shows the sensor coordinate system inclined with respect to the horizontal coordinate system. It is a figure which shows the relationship between the rotation angle when rotating an acceleration sensor, the sensor output in each measurement azimuth | direction, a dynamic error, a static error, and an inclination error. It is a block diagram of the terminal device and measurement terminal device which are shown in FIG. It is a characteristic view which shows the relationship between the value (vertical axis | shaft) and the rotation angle which normalized the measured value obtained by the X-axis acceleration sensor in the biaxial 4 direction rotation measurement. It is a characteristic view which shows the relationship between the value (vertical axis | shaft) and the rotation angle which normalized the measured value obtained by the orthogonal biaxial (X-axis and Y-axis) acceleration sensor in the biaxial 4 azimuth | direction rotation measurement. It is description which shows the inclination azimuth of the input I based on a gravitational acceleration. It is a figure which shows the measured value obtained with the orthogonal biaxial (X-axis and Y-axis) acceleration sensor by the biaxial 4 azimuth | direction rotation measurement. It is a figure which shows the primary processing data which subtracted the dynamic error from the output obtained by the orthogonal biaxial (X axis and Y axis) acceleration sensor in the biaxial 4-azimuth rotation measurement. It is a figure which shows the secondary processing data (tilt error) which subtracted the dynamic error and the static error from the output obtained by the orthogonal two-axis (X-axis and Y-axis) acceleration sensor in the two-axis four-azimuth rotation measurement. FIG. 13 is a diagram showing normalized tertiary processing data obtained by dividing the data shown in FIG. 12 by an inclination amount Iφ. It is a figure which replaces the tertiary processing data normalized by the inclination amount Iφ on the complex plane. It is a figure explaining the feather coordinate which shows inclination azimuth in a real number component and an imaginary number component. It is a figure which shows the relationship between the tertiary processing data calculated by biaxial 4 direction rotation measurement, and inclination | tilt azimuth angle (theta). It is a figure which shows the relationship between the normalized value of the acceleration collected by the biaxial 2-azimuth | direction rotation measurement, and an azimuth | direction. It is a figure which shows the measured value of the acceleration collected by 2 axis | shaft 2 azimuth | direction rotation measurement. It is a figure which shows the primary processing data calculated by biaxial 2 direction rotation measurement. It is a figure which shows the secondary processing data calculated by biaxial 2 direction rotation measurement. It is a figure which shows the example of calculation of the secondary process data calculated by biaxial 2 azimuth | direction rotation measurement. It is a figure which shows the tertiary processing data calculated by biaxial 2 azimuth | direction rotation measurement. It is a figure which shows norm I (phi), sin (theta), cos (theta), and tan (theta) calculated by biaxial 2 azimuth | direction rotation measurement. It is a figure which shows the relationship between the tertiary processing data calculated by biaxial 2 azimuth | direction rotation measurement, and inclination | tilt azimuth angle (theta). It is a figure which shows a North-East-Down (NED) coordinate system. It is a figure which shows the output noise analysis of an acceleration sensor. Rotational section t _S, is a view for explaining the measurement period t _R and 1 cycle interval. It is a figure which shows the several cycle which made the direction set initially in each cycle the same. It is a figure which shows the several cycle which varied the direction initially set in each cycle. It is a figure which shows the modification of FIG. It is a figure for demonstrating inclination azimuth angle (theta) phi, the difference (psi) n of measurement azimuth | direction and inclination azimuth angle, measurement azimuth angle (theta) n, and virtual plane P ( _phi ). It is a figure for demonstrating inclination | tilt angle (phi) and inclination amount (Iphi). It is a figure which shows primary processing data. It is a figure which shows secondary processing data. It is a figure which shows how to obtain | require an azimuth angle direction. It is a figure which shows the temperature dependence of a static error. It is a flowchart which shows the update operation | movement of a correction value. It is a flowchart which shows inclination measurement operation | movement. It is a figure which shows the example which implements data collection in multiple cycles, changing a reference azimuth | direction in each cycle. It is a figure which shows the other example which implements data collection in multiple cycles, changing a reference azimuth in each cycle. It is a figure which shows the operation | movement flow which collects data after waiting time from a measurement start command.

  Hereinafter, preferred embodiments of the present invention will be described in detail with reference to comparative examples. The present embodiment described below does not unduly limit the contents of the present invention described in the claims, and all the configurations described in the present embodiment are indispensable as means for solving the present invention. Not necessarily.

1. Measurement System The measurement system shown in FIG. 1 includes a host device 1 that centrally manages measurement data, a plurality of terminal devices 2 that are connected to the host device 1 via, for example, the Internet, wireless, or mobile phones, and each terminal device 2 that is connected to, for example, WiFi. (Registered trademark) or wireless communication such as Bluetooth (registered trademark), a mobile communication system, or one or a plurality of measurement terminal devices 3 connected by a local area network (LAN). The terminal device 2 may be a general-purpose machine such as a mobile phone, a smartphone, a tablet, or a terminal PC, or a dedicated machine. The measurement terminal device 3 may be a general-purpose device such as a device connected to or built in an acceleration sensor, a mobile phone, a smartphone, a tablet, or a terminal PC, or a dedicated device or an acceleration measuring device.

  In each measurement terminal 3, initial calibration at the time of installation and periodic maintenance calibration are performed. This is because each measurement terminal 3 has a drift due to a change over time or an environmental change, or an error due to an inclination of the installation surface. In order to perform the calibration, a calibration program (including an error measurement program, an inclination measurement program, a bias correction program, etc.) is stored in the storage device of the host device 1 or each terminal device 2. Calibration at each measurement terminal 3 is executed according to a calibration program. The calibration program may be transmitted from the host device 1 to the terminal device 2.

  The measurement terminal device 2 shown in FIG. 2 has the triaxial (X, Y, Z) acceleration sensors 10x, 10y, and 10z shown in FIG. 3 inside the housing 4 having the bottom surface 4A as an installation surface. Note that the output of the acceleration sensor 10z is not used for error measurement or tilt angle / tilt azimuth angle measurement, and one or both of the biaxial acceleration sensors 10x and 10y can be used as described later. In other words, the present embodiment is effective as long as the inclination angle φ is not excessively large and can be measured without using the output of the acceleration sensor 10z.

  In the coordinates X, Y, and Z of the triaxial acceleration sensors 10x, 10y, and 10z, the XY plane (also referred to as a virtual plane) including the orthogonal X and Y axes is parallel to the bottom surface 4A, and the Z axis is the XY plane. Orthogonal to The casing 4 is provided with a rotation operation unit 5 and an indicator (LED or the like) 6. The operator can be instructed by the lighting or blinking of the indicator 6 in the measurement terminal 2 in order to execute the process according to the calibration program. When the rotation operation unit 5 is rotated according to the instruction, the three-axis acceleration sensors 10x, 10y, and 10z are rotated around the normal line (Z axis) orthogonal to the bottom surface (installation surface) 4A. In particular, in order to perform periodic maintenance calibration unattended, instead of the rotation operation unit 5 or in addition to the rotation operation unit 5, a rotation drive unit 8 such as a motor for automatically rotating the above-described shaft (FIG. 6). Reference) may be provided. Specifically, the acceleration sensor can be rotated from the outside of the housing 4 with a knob, and there is a click so that the knob stops in the required direction. There is also a trigger input unit that notifies the program of the start of calibration work by rotation. There is a display section for displaying a time when the rotation can be performed and indicating that the calibration work is completed. There is also an input unit for instructing application of the acquired calibration value.

2. Error superimposed on the output of the acceleration sensor FIG. 4 shows a horizontal coordinate system (Xr, Yr, Zr) and a sensor coordinate system (X, Y, Z). The (Xr-Yr) plane including the orthogonal two axes Xr, Yr of the horizontal coordinate system (Xr, Yr, Zr) is a horizontal plane, and the Zr axis is a vertical axis orthogonal to the horizontal plane (Xr-Yr).

  As shown in FIG. 4, the Zr axis (vertical axis) of the horizontal coordinate system (Xr, Yr, Zr) and the Z axis of the sensor coordinate system (X, Y, Z) are tilt angles φ, and the sensor coordinate system ( It is assumed that the (XY) plane of (X, Y, Z) is inclined with respect to the (Xr-Yr) plane of the horizontal coordinate system (Xr, Yr, Zr). When the three-axis acceleration sensors 10x, 10y, and 10z are rotated around the Zr axis by the rotation operation unit 5, the gravitational acceleration G acting along the Zr axis is a circle, an ellipse, or the like centered on the Z axis as shown in FIG. Draw a straight line C. The size of the circle, ellipse, or straight line C can be obtained from one or both of the measured values Dx and Dy of the biaxial acceleration sensors 10x and 10y that are rotated and stopped. In addition, when the straight line intersecting the (XY) plane and the (Xr-Yr) plane is parallel to either Xr or Yr, the gravitational acceleration G acting along the Zr axis is a straight line centering on the Z axis. Draw a trajectory. The size of this straight line can be obtained from one or both of the measured values Dx and Dy. In the coordinate system (X, Y, Z) of the acceleration sensors 10x, 10y, 10z, the acceleration X and the acceleration Y are right-handed coordinates, and Y is counterclockwise with respect to X when viewed from the −Z direction. The direction is 90 degrees.

  The output axes of the acceleration sensors 10x, 10y, and 10z can be set as the reference azimuth with the first measurement azimuth determined by associating the azimuth with the North-East-Down (NED) coordinate system shown in FIG. The reference direction of the sensor projected on the horizontal plane indicated by the NE plane shown in FIG. 25 is associated with the orientation in the NE plane of the NED coordinate system. Since the inclination azimuth angle ψ is obtained by the acceleration sensors 10x, 10y, and 10z, the inclination azimuth angle ψ is the place where the acceleration sensors 10x, 10y, and 10z are installed, and the NED coordinate system of the installation place and the acceleration sensors 10x, 10y, and 10z. Since the output axis directions are associated with each other, the direction of inclination can be indicated. That is, as shown in FIG. 25, an angle formed by the projection direction of the reference direction output of the acceleration sensor onto the horizontal plane and the reference direction of the NED coordinate system is represented by ψ.

Here, when the three-axis acceleration sensors 10x, 10y, and 10z are stationary, the input I is a gradient component of the gravitational acceleration G. The norm Iφ of the bias shift on the XY plane of the acceleration G due to the tilt angle φ is
It becomes. Further, as shown in FIG. 4, the crossing angle between the X axis and Iφ is defined as a tilt azimuth angle θ. The measured value Dx of the acceleration sensor 10x and the measured value Dy of the acceleration sensor 10y can be expressed by the following equations using the norm Iφ and the tilt azimuth angle θ.

In reality, errors due to drift are superimposed on the measured values of the acceleration sensors 10x and 10y. This drift is defined as follows.

Here, when the three-axis acceleration sensors 10x and 10y are stationary, the input I is only the gradient component Iφ of the gravitational acceleration G, so the equation (5) becomes the following equation (6).

From the output noise analysis of the acceleration sensor shown in FIG. 26, the section _AB with the main flicker noise _DRB is selected as the average section at the time of data acquisition. Adjust the rate white noise D _RN to be longer than the minimum measurement interval. By selecting the average calculation interval of the measurement data in this way, high-precision measurement data with less rate white noise _DRN can be obtained. The noise whose drift increases as the average interval becomes longer, such as rate random walk noise _DRR , is adjusted to be equal to or less than the time length of the measurement interval that is minimized in the data measurement environment. By selecting the average calculation interval of the measurement data in this way, highly accurate measurement data with less rate, random, walk, and noise _DRR can be obtained. Since flicker noise D _RB can not be removed, and then optimized so that the measurement time is not unnecessarily long. Therefore, unlike the average value section of the data, it is desirable to select so that the entire cycle measured by changing the direction falls within the longest of the appropriate section. Measurement conditions are desirable that the measurement time of the A-B section random drift rate D _R becomes minimum.

The drift rate E due to the environment is expressed as offsets Dx _ΔT ΔT and Dy _ΔT ΔT due to temperature drift during measurement. From the above, the measured value Dx of the acceleration sensor 10x and the measured value Dy of the acceleration sensor 10y are expressed by the following equations (7) and (8) in consideration of errors.

In the model of Expression (7), when the acceleration sensor 10x is rotated, the relationship between the rotation angle (horizontal axis) and the output (vertical axis) is as shown in FIG. The amplitude of the measured value Dx of the acceleration sensor 10x shown in FIG. 5 depends on the inclination angle φ. The model of Formula (8) is the same. Here, since DFx and DFy are substantially constant at each stationary position before and after rotation, they are also referred to as static errors. On the other hand, offsets Dx _ΔT ΔT and Dy _ΔT ΔT due to temperature drift are also referred to as dynamic errors because they differ at each stationary position before and after rotation. In FIG. 5, the temperature drift Dx _ΔT ΔT is shown as a constant rate. Although the actual temperature drift Dx _ΔT ΔT is expected not to be a constant rate, it is shown here by approximating a constant rate. Further, since the inclination components Iφ · cos θ and Iφ · sin θ of the gravitational acceleration G are superimposed on the sensor output as errors due to inclination, they are referred to as inclination errors.

3. Terminal Device and Measurement Terminal Device FIG. 6 shows a terminal device 2 and a measurement terminal device 3. The measurement terminal device 3 includes three-axis acceleration sensors 10x, 10y, and 10z, a rotation operation unit 5, an indicator 6, and a communication device 7. The terminal device 2 may have the rotation drive unit 8 described above. Moreover, the measurement terminal device 3 may have the rotation operation part 5 and the rotation drive part 8 outside.

  The terminal device 2 composed of a terminal PC or the like has a storage device 20 that stores the above-described calibration program (error measurement program, inclination measurement program, bias correction program, etc.). Error measurement, inclination measurement, and bias correction performed in the terminal device 2 are performed according to a calibration program.

  For example, the terminal device 2 includes a rotation command unit 30, an error measurement unit 40, an inclination measurement unit 50, an inclination bias correction unit 60, a communication device 70, and the like that are executed and controlled according to a calibration program. The rotation command unit 30 generates a rotation command to be transmitted to the measurement terminal device 3 via the communication device 70 according to the calibration program.

  The error measurement unit 40 measures the error superimposed on the output of the acceleration sensors 10x and 10Y based on the output from the measurement terminal device 3, and the error measurement unit 40 measures the drift (dynamic error). An error measuring unit 41, a static error measuring unit 42 for measuring a bias (static error), and a tilt error for measuring a tilt error by removing dynamic errors and static errors from outputs of the acceleration sensors 10X and 10Y, for example. And a measurement unit 43. If the static error can be removed in the process of processing the outputs of the acceleration sensors 10X and 10Y, the static error measuring unit 42 is not necessary or can be unused.

  The inclination measuring unit 50 measures the inclination (inclination angle, inclination direction) from data obtained by removing dynamic errors and static errors from the outputs of the acceleration sensors 10X and 10Y, for example. The inclination measuring unit 50 includes an inclination angle measuring unit 51 and an inclination azimuth measuring unit 52.

  These rotation command section 30, error measurement section 40 (dynamic error measurement section 41, static error measurement section 42, tilt error measurement section 43), slope measurement section 50 (tilt angle measurement section 51, tilt azimuth angle measurement section 52) ) Is clarified by various rotation measurement methods described below.

The tilt bias correction unit 60 uses the tilt error obtained by the tilt error measurement unit 43 as a tilt bias, and removes the tilt bias from the output from the acceleration sensor when detecting acceleration.
4). Error Measurement Method In the following, dynamic errors Dx _ΔT ΔT, Dy _ΔT ΔT at the rotational position (static position) set by operating the rotary operation unit 5 according to the calibration program, static errors DFx, DFy, and tilt error Iφ · A method for measuring cos θ, Iφ · sin θ will be described.

In the present embodiment, the measurement method is defined as follows.
(I) The direction of the detection axis of the acceleration sensor set at the time of measurement is referred to as a measurement direction. At least one measurement azimuth (reference azimuth) is measured in an overlapping manner, and measurement is also performed at an azimuth different from the reference azimuth. Preferably, the first and last measurement directions are set as the reference directions.

(Ii) Since there are four unknowns in the equations (7) and (8) (for example, four in the equation (7), Iφ, cos θ, DFx, and Dx _ΔT ΔT), the acceleration sensor has at least 4 detection axes. Measure with more than one measuring direction (stationary position). That is, the unknowns are the tilt error Iφcos θ, the bias (static error) DFx, and the drift (dynamic error) Dx _ΔT ΔT, and these errors are obtained. However, if the outputs of the biaxial acceleration sensors 10x and 10y are used, two measurements in one measurement direction can be counted.

(Iii) Although the rotation angle between measurements can be determined arbitrarily depending on the number of measurement directions, the rotation angle between measurements is preferably set in increments of 90 degrees or 180 degrees for the convenience of calculation.
When the rotation angle between measurements is 90 ° or 180 °, the biaxial 2-azimuth rotation measurement (measurement azimuth is 0 °, 180 °, 360 °) and the biaxial 4-azimuth rotation measurement (measurement azimuth is 0 Degrees, 90 degrees, 180 degrees, 270 degrees, 360 degrees).

4.1. FIG. 7 shows measured values of the acceleration sensor 10x for each measurement direction (0 degree, 90 degrees, 180 degrees, 270 degrees, 360 degrees) when measured in two axes and four directions. As shown in FIG. 7, when the measured values are the same at 0 degrees and 360 degrees, it is assumed that the drift in the output of the acceleration sensor 10x is stable during this measurement. Assuming that the drift during measurement is stable, the measurement values in four directions orthogonal from the 0 degree azimuth to the +270 degree azimuth are the amount of inclination of the measurement system at the time of measurement and the acceleration sensor 10x (or 10y). It is assumed that it is the sum of offsets due to the drift (static error). If the value varies between 0 degrees and 360 degrees, it is necessary to assign the difference equally to each measurement as a dynamic error for subtraction (removal of dynamic error). The average value of measured values in four orthogonal directions of an arbitrary detection axis indicates an offset amount due to bias drift. The locus with respect to the rotation direction of the output in four directions orthogonal to any detection axis is four points on the sine curve as shown in FIG. 7, and the amplitude thereof is an inclination with respect to the horizontal plane. Moreover, the azimuth | direction which takes the maximum value and minimum value shown in FIG. 7 becomes the azimuth | direction of the inclination.

  In addition, the vertical axis | shaft of FIG. 7 is normalized not to the measured value itself but to the ratio (amplitude ± 1) of the maximum expected amplitude and the measurement result. If the (XY) plane of the sensor coordinate system (X, Y, Z) is parallel to the horizontal plane, the values on the vertical axis in FIG. Similarly to FIG. 7, the outputs of the orthogonal biaxial acceleration sensors 10x and 10y are as shown in FIG. As shown in FIG. 8, the phases of the outputs of the orthogonal biaxial acceleration sensors 10x and 10y are shifted by 90 degrees.

  Here, the (XY) plane of the sensor coordinate system is defined as shown in FIG. The Y axis is 90 degrees counterclockwise with respect to the X axis direction. The rotation direction of the acceleration sensor is, for example, counterclockwise, and is rotated in the direction of 0 degrees → 90 degrees → 180 degrees → 270 degrees → 0 degrees (360 degrees). When releasing, it can be returned clockwise so that the internal wiring does not stretch.

As shown in FIG. 9, the inclination azimuth angle from the 0 degree direction is θ, the inclination amount is I, the measurement order is n (n = 0, 1, 2, 3), and the measurement azimuth is n · π / 2. Then, each measured value shown in Equations (7) and (8) is as follows.
For example, the measured value in the 0 degree direction when n = 0 is represented by the following equation (9 (10)) when the error is expressed as Xe, Ye.

4.1.1. Measurement procedure 1 (2-axis 4-direction data collection)
First, the rotation operation unit 5 shown in FIG. 2 is operated to rotate the orthogonal biaxial acceleration sensors 10x and 10y. For example, each measurement azimuth in the order of 0 degrees → 90 degrees → 180 degrees → 270 degrees → 0 degrees (360 degrees). Stop at. In each measurement direction, the biaxial 4-direction data is collected by the acceleration sensors 10x and 10y in a stationary state. Two-axis four-direction data is defined as shown in FIG.

4.1.2. Measurement procedure 2 (dynamic error measurement)
Next, drifts Dx _ΔT ΔT and Dy _ΔT ΔT during measurement, which are dynamic errors, are measured. As described above with reference to FIG. 7, if the first (0 degree) and last (360 degree = 0 degree) measurement values are equal, the drift during measurement can be ignored, but if there is a fluctuation, the first (0 degree) The drifts Dx _ΔT ΔT and Dy _ΔT ΔT can be obtained from the difference between the measured values at the last and 360 degrees. This is because, as can be seen from the equations (7) and (8), the measured values X0 and X4 having the same measurement azimuth at 0 degrees differ only in the drift Dx _ΔT ΔT, and the other measured values of Iφ · cos θ and DFx are measured values This is because both X0 and X4 are equal. In the present embodiment, the reason why the first and last measurement orientations are made equal is to enable measurement of drift (dynamic error) in all measurement orientations.

  Here, the measurement azimuth is 0 degree, and the difference between the measurement values X0 and X4 is the same, and the difference between the dynamic errors in the measurement values X0 and X4. The difference in the dynamic error may be a change in inclination during measurement, temperature characteristic fluctuation, environmental vibration change, etc., but the measurement itself is performed in a relatively short time, and the measurement timing is also stable with little environmental temperature fluctuation. By selecting the time period during which measurement is performed, and by setting the conditions for stabilizing the change in current consumption of the measurement terminal during measurement, the time can be reduced to almost negligible. Therefore, the dynamic error of the first 0 degree measurement azimuth is zero, and the last 360 degree three measurement azimuth has the maximum or minimum dynamic error, with 90, 180, and 270 degrees between each measurement azimuth. Can be assigned based on the difference between the measured values X0 and X4.

For example, as described above, when the drifts Dx _ΔT ΔT and Dy _ΔT ΔT being measured are approximated at a constant rate (slope), the difference (X4−X0) between the first (0 degree) and the last (360 degree) measurement values. Is linearly complemented, the drift (dynamic error) superimposed on the nth measurement value Xn can be expressed as n (X4−X0) / 4. In this way, it is possible to measure the drift (dynamic error) superimposed on the measurement values in all measurement directions. The data Xn ′ from which the drift (dynamic error) is excluded from the nth measurement value Xn is shown as follows. Further, primary processing data Xn′Yn ′ from which drift (dynamic error) is excluded from the measured values shown in FIG. 10 is as shown in FIG.

4.1.3. Measurement procedure 3 (Static error measurement)
If the notation shown to Formula (9) (10) is used, measured value X0-X3 can be shown as follows.

The average of the measured values of X0 to X3 is
It becomes. In the parenthesis of the first term on the right side, from the symmetry as the premise of measurement,
From this, the following equation is established.
From the above, the following equation is established.
In this way, by adding and averaging the measurement values of the orthogonal measurement directions (0 degrees, 90 degrees, 180 degrees, and 270 degrees), the value of the sine wave or cosine wave component is eliminated, and only the error Xe is extracted. be able to.

Since the error _{Xe = DFx + DRx + Dx ΔT} ΔT or error _{Xe = DFy + DRy + Dy ΔT} ΔT, instead XAVG, calculate the X'avg.
Since the data X ′ has the dynamic errors Dx _ΔT ΔT and Dy _ΔT ΔT removed, the average value X′avg also does not include the dynamic errors Dx _ΔT ΔT and Dy _ΔT ΔT (Xe−Dx _ΔT ΔT) or (Xe−Dy _ΔT ΔT) can be obtained. If the random drifts DRx and DRy can be ignored as described above, the average value X′avg = DFx or the average value Y′avg = DFy, and the static error DFx is determined by the average value X′avg or Y′avg. Or it can be seen that DFy is obtained.

4.1.4. Measurement procedure 4 (measurement of tilt error)
Next, in order to further remove the static error DFx from the data X ′ from which the dynamic error has been removed, the following equation is calculated to obtain the secondary processing data shown in FIG.
The secondary processing data X ″ n thus obtained is obtained by subtracting the dynamic error Dx _ΔT ΔT and the static error DFx from the measured value X, and X ″ n = Iφ · cos θ is inclined from the equation (7). It is calculated as an error. Similarly, Y ″ n = Iφ · sin θ is obtained as a tilt error from the equation (8).

  As described above, all of the dynamic error, static error, and tilt error can be obtained from the biaxial 4-azimuth data.

4.1.5. Measurement procedure 5 (Measurement of tilt angle φ)
The obtained secondary machining data X ″ n is shown using the measurement order n as follows.
Using this equation, the relationship between the secondary machining data X ″ n obtained in the procedure 4 is as follows.
In order to reduce the measurement error etc., the average is calculated with the following combinations.
Since X ″ ₀₂ and X ″ ₁₃ are orthogonal to each other, the inclination amount Iφ is calculated from these two values as follows.
Since this inclination amount Iφ is a projection of the inclination angle φ onto the horizontal plane, the inclination angle I _φangle is as follows.
When the measured value is in G units, the tilt angle φ is expressed as follows.
As described above, the tilt angle φ can be obtained from the biaxial 4-azimuth data.

4.1.6. Measurement procedure 6 (Measurement of tilt azimuth angle θ)
First, the secondary machining data X ″ n obtained in the procedure 4 is divided by the inclination amount Iφ obtained in the procedure 5 according to the following equation to obtain the tertiary machining data shown in FIG.
This tertiary processed data is X ″ ′ = cos θ and Y ′ ″ = sin θ, which means a sine wave or cosine wave normalized to amplitude ± 1 shown in FIG.

As shown in FIG. 14, this sine wave or cosine wave is rearranged into orthogonal coordinates on the Gaussian plane, and the polarity is given in consideration of the measurement direction.
The equation (12) is transformed using the equation (11), and averaged for every real number of X and Y and every imaginary number of X and Y shown in FIG. Thereby, the complex number representation of the X-axis and the Y-axis is as follows.

The norm of the complex number of the X axis and the Y axis shown in Expression (18) is 1 as shown in the following expression.
For example, the relationship between the real number and imaginary number of the X axis and the norm is as shown in FIG. 15, and the following equation is established from the real number and the imaginary number for the tilt azimuth angle θ from FIG.

From the values that can be taken in each section of the first to fourth quadrants shown in FIG.
First quadrant θs> 0, θc> 0 Result θ = θc, θs = θc
Second quadrant θs> 0, θc> 0 Result θ = θc, θs ≠ θc
Third quadrant θs <0, θc> 0 Result θ = 2π− ≠ θc, θs = θc
Fourth quadrant θs <0, θc> 0 Result θ = 2π−θc, θs ≠ θc
As a result, when θs> 0 and θc> 0, the following equation is established (unit is radian).
Similarly, when θs> 0 and θc> 0, the following equation is established (unit is radian).
From the above, the tilt azimuth angles θxn and θyn are as shown in FIG. The average value of the tilt azimuth angles θxn and θyn shown in FIG. 16 can also be calculated.
The X average value θ _avg-x and the Y average value θ _avg-y are assumed to be the same value as a premise, but they may be different values due to various factors, but are approximately equal.
As described above, the solutions can be obtained for all four unknowns in the equations (7) and (8) by the measurement procedures 1 to 6.

4.2. 2-axis 2-azimuth rotation measurement 4.2.1. Measurement procedure 1 (2-axis 2-azimuth data collection)
First, the rotation operation unit 5 shown in FIG. 2 is operated to rotate the orthogonal biaxial acceleration sensors 10x and 10y, and stopped at each measurement direction in the order of 0 degrees → 180 degrees → 0 degrees (360 degrees). In each measurement azimuth, measurement values in two axes and two azimuths are collected by the acceleration sensors 10x and 10y in a stationary state. FIG. 17 shows measured values of the acceleration sensor 10x for each measurement direction (0 degrees, 180 degrees, 360 degrees) when measured in two directions and two directions (Y-axis is omitted). As in the biaxial 4-azimuth rotation measurement shown in FIG. 7, if the values are the same at 0 degrees and 360 degrees, it is assumed that the drift in the output of the acceleration sensor 10x is stable during this measurement. If there is a variation, the difference is assigned to each measurement as a dynamic error and subtracted. Note that the vertical axis in FIG. 17 is normalized not to the measurement value itself as in FIG. 7 but to the ratio between the expected maximum amplitude and the measurement result (amplitude ± 1). Two-axis two-direction data is defined as shown in FIG.

4.2.2. Measurement procedure 2 (dynamic error measurement)
Next, the drifts Dx _ΔT ΔTn and Dy _ΔT ΔTn during measurement, which are dynamic errors in the equations (7) and (8), are measured. As described above with reference to FIG. 17, if the first (0 degree) and last (360 degree = 0 degree) measurement values are equal, drift during measurement is negligible, but if there is a fluctuation, biaxial four-direction rotation measurement procedure in the same manner as in 2 (4.1.1) of the measurement, the first (0-degree) and the last (360) of the measured value differences from the drift Dx _{[Delta] T} .DELTA.Tn of, it is possible to determine the Dy _{[Delta] T} .DELTA.Tn.

Here, the difference between the measurement values X0 and X2 that are equal to each other at the measurement azimuth of 0 degrees is the difference in dynamic error in the measurement values X0 and X2. The dynamic error of the first 0 degree measurement direction is zero, the dynamic error is the maximum or minimum at the last 360 degree measurement direction, and the dynamic error at the 180 degree measurement direction is measured value X0. , X2 can be assigned based on the difference. For example, when the drifts Dx _ΔT ΔTn and Dy _ΔT ΔTn being measured are approximated at a constant rate (slope) as described above, the difference (X2−X0) between the first (0 degree) and the last (360 degree) measurement values Is linearly complemented, the drift (dynamic error) superimposed on the n-th measurement value Xn can be expressed as n (X2−X0) / 2. In this way, it is possible to measure the drift (dynamic error) superimposed on the measurement values in all measurement directions. The data Xn ′ from which the drift (dynamic error) is excluded from the nth measurement value Xn is shown as follows. Further, primary processed data Xn ′ and Yn ′ from which drift (dynamic error) is excluded from the measured values shown in FIG. 18 are as shown in FIG.

4.2.3. Measurement procedure 3 (Static error measurement)
The static error DFx is obtained from the average of X′0 and X′1 defined by the equation (13) in the same manner as in the processing procedure 3 (4.1.3) of the biaxial 4-azimuth rotation measurement, and Y ′ The static error DFy is obtained from the average of 0 and Y′1.

4.2.4. Measurement procedure 4 (measurement of tilt error)
Next, in order to further remove the static error DFx from the primary machining data X ′ from which the dynamic error has been removed, the following equation is calculated to obtain the secondary machining data shown in FIG.
The secondary processing data X ″ n thus obtained is obtained by subtracting the dynamic error Dx _ΔT ΔT and the static error DFx from the measured value X, and X ″ n = Iφ · cos θ is inclined from the equation (7). It is calculated as an error. Similarly, Y ″ n = Iφ · sin θ is obtained as the tilt error from the equation (8). By calculating the equation (16), the tilt errors X ″ n and Y ″ n in each measurement direction are obtained as shown in FIG. It becomes street.
As described above, all of the dynamic error, static error, and tilt error can be obtained from the biaxial, two-azimuth rotation measurement.

4.2.5. Measurement procedure 5 (Measurement of tilt angle φ)
The secondary processing data X ″ n, Y ″ n obtained in the processing procedure 4 is transformed as follows to obtain X ″ 0, X ″ 1, Y ″ 0, Y ″ 1.

From the above, the following equation is established.
In order to reduce the measurement error and the like, the X axis and the Y axis are averaged by the following equations, respectively. In the following equation, averaging is performed in consideration of positive and negative signs.
The following formula is obtained by calculating the above formula.

Since X ″ 01 and Y ″ 01 are orthogonal to each other, the inclination amount Iφ can be calculated from these two values according to the following equation.
Since the tilt amount Iφ is a projection of the tilt angle φ onto the horizontal plane, the tilt angle φ can be obtained in the same manner as in the equations (12) and (13) of the biaxial four-direction rotation measurement.
As described above, the tilt angle φ can be obtained from the biaxial 2-azimuth data.

4.2.6 Measurement procedure 6 (Measurement of tilt azimuth angle θ)
First, each secondary machining data X ″ n obtained in the procedure 4 is divided by the inclination amount Iφ obtained in the procedure 5 and normalized as shown in the equation (14) to obtain the tertiary machining data X ″ shown in FIG. 'N is calculated.
Next, regarding the tertiary processed data of 0 degree and 180 degrees, the complex number V is expressed as follows with the X axis as a real number and the Y axis as an imaginary number.

FIG. 23 shows the complex norm, sin θ, cos θ, and tan θ shown in FIG. 15 using the complex number V for the tertiary processed data of 0 degrees and 180 degrees. Further, the tilt azimuth angles θxn and θyn are as shown in FIG. The average value of the tilt azimuth angles θxn and θyn shown in FIG. 24 can also be calculated.
The X average value θavg-x and the Y average value θavg-y are assumed to be the same value as a premise, but they may be different values due to various factors, but are approximately equal.
As described above, the solutions can be obtained for all four unknowns in the equations (7) and (8) by the measurement procedures 1 to 6 even in the biaxial two-direction rotation measurement. Compared with the biaxial 4-azimuth rotation measurement, the number of data is smaller in the 2-axis 2-azimuth rotation measurement, so the accuracy deteriorates. However, the measurement amount is about ½, so the measurement load is reduced.
4.3. General method of rotation measurement including rotation angle other than integer multiple of 90 degrees In the above-described embodiments, the rotation angle of the acceleration sensor is set to an integer multiple of 90 degrees. Hereinafter, rotation angles other than an integer multiple of 90 degrees are used. A general method of azimuth rotation measurement including the will be described.

4.3.1. Processing procedure 1 (data collection)
Measure continuously in a stationary state by rotating the detection axis of the acceleration sensor and changing the direction. As shown in FIG. 27, a pair of an interval t _{S in} which the detection axis of the acceleration sensor is rotated and directed in a desired direction and an interval t _{R in} which acceleration is measured during a stationary state constitutes one-way measurement. . This measurement in one direction is repeated, and measurement is continuously performed while changing the direction by rotating the detection shaft. An interval of data processing for measuring an error is cut out from continuous measurement data measured while changing the measurement direction, and this is defined as one cycle. The measurement direction is measured in angular steps obtained by dividing the circumference (2π) by a natural number of 3 or more. The direction from the center of the circle to the vertex of the regular polygon inscribed in the circle is taken as the measurement direction. One cycle interval of m = 0,1,2, ..., and _{m m.} 1 cycle interval, a first measurement direction (reference direction) m = 0 interval, other and the direction of measurement which is rotated from this direction, until the measurement m = m _m in the same direction as the first measuring direction (reference direction) It is set as the section. The azimuth set in this one-cycle section is the first azimuth (reference azimuth), the last azimuth that is the same direction as the reference azimuth, and the other azimuths, which are all necessary to measure the error. Includes orientation. All orientations necessary for measurement are included once or more in one cycle. Accordingly, the length of one cycle section may be different. The direction of rotation for changing the direction may be reversed alternately. Further, the rotations of adjacent cycle sections may be symmetric in the direction order in the cycle sections, or may be in the same order.

  As shown in FIGS. 28 to 30, for example, the number of directions required for error measurement is five, the directions are a, b, c, d, e, and f, and these five directions are [0: 2π]. Suppose that it is in range. As shown in FIGS. 28 to 30, s = 0, 1, 2,... Are measured when continuously measured while rotating and changing the direction. 28 to 30, the rotation direction at each time of s = 0, 1, 2,... May be the same direction, or may be alternately reversed.

  In FIG. 28 and FIG. 29, for example, in the k-th cycle, after measurement of S = 14, it is determined that one cycle is established, and a k cycle section is established. The error evaluation process described later is performed for the established k cycle interval. The first and last cycle are in the same direction. In FIG. 28, the initial direction of all cycles is the same in direction a, but adjacent cycles in FIG. 29 differ in the initial direction of the cycle. In FIG. 30, the first and last cycles are in the same direction, but five directions (a, b, c, d, e, f) are set twice each in one cycle.

Note that, as described above, the detection axis of the acceleration sensor can be set to have the first measurement direction determined in association with the North-East-Down (NED) coordinate system shown in FIG. 25 as the reference direction. A detection axis of an acceleration sensor having a detection axis on a virtual plane that intersects the direction of gravity is generally a horizontal plane. As shown in FIG. 25, an angle formed by the projection direction of the reference direction output of the acceleration sensor onto the horizontal plane and the reference direction of the NED coordinate system is denoted by ψ. The direction is determined by associating the reference direction of the measurement direction of rotation measurement with the North-East-Down (NED) coordinate system of the environment where the acceleration sensor is installed. Further, as shown in FIG. 26, the measurement condition is desirable that the measurement time of the A-B section random drift rate D _R becomes minimum.

4.3.2. Processing procedure 2 (dynamic error measurement)
The measurement result is a relationship in which each parameter is expressed by the following model formula. Each term is estimated from the measurement data.

Here, FIG. 31 shows the tilt azimuth angle θφ, the difference between the measurement azimuth angle and the tilt azimuth angle ψn, and the measurement azimuth angle θn in the above formula. The acceleration sensor has a detection axis in the virtual plane P _phi (Fig. 31) intersecting the direction of gravity, when rotated about the normal line of the plane P _phi, the maximum angle which is inclined relative to the horizontal plane P _H As shown in FIG. 32, the inclination angle φ is set, and the gravitational acceleration component output to the detection axis of the acceleration sensor at this time is set as the inclination amount Iφ. The amount of inclination Iφ due to the inclination angle φ of the gravitational acceleration is the same as the above-described equation (1) as follows.

Here, the inclination amount Iφ has a relationship between the direction of the inclination and the direction on the virtual plane _Pφ when the acceleration sensor output axis is set as the reference orientation as the following formula with respect to the reference direction.

For the measured data of one cycle, the order m of the measurement data is m = 0, 1, 2,..., M _m , the mth acceleration sensor output is Dm, and the measurement azimuth is θm. First measurement direction of one cycle data section (reference azimuth) and m = 0, the last measurement direction (reference direction) and m = m _m. The difference between the first data m = 0 and the last data m = m _m in the reference direction of the measurement unit section is obtained, and the difference is evenly distributed during the measurement to the respective measurement data. Find the dynamic error. The dynamic error is subtracted from the output Dm of the mth acceleration sensor.

As described above, with respect to the data obtained by subtracting the dynamic error, the measurement values in which the measurement azimuth overlaps in one cycle of the measurement interval can be averaged in the same azimuth and data for each measurement azimuth angle can be obtained.
The data for each measurement azimuth is a combination of the measurement value Dn divided by the measurement azimuth number n and the measurement azimuth angle θn, and these are the primary processed data Dn ′ shown in FIG.

4.3.3. Processing procedure 3 (Static error measurement)
Next, an average value of the primary processing data is calculated to calculate a static error _DF . However, measuring the azimuth number n = 0,1,2, ..., a _{n n,} measurement orientation number is _{n n.}

4.3.4. Processing procedure 4 (generation of secondary processing data)
The static machining error _DF is subtracted from the primary machining data Dn ′ to generate secondary machining data Dn ″. This secondary machining data is shown in FIG.

The secondary machining data X ″ m obtained in this way is obtained by subtracting the dynamic error Dx _ΔT ΔT and the static error DFx from the measured value X, and X ″ m = Iφ · cos θ is inclined from the equation (7). It is calculated as an error. Similarly, Y ″ m = Iφ · sin θ is obtained as a tilt error from the equation (8).

4.3.5. Processing procedure 5 (calculation using secondary machining data)
The relationship between the measurement azimuth angle θn and the secondary machining data Dn ″ is expressed by the following equation.

Since the measurement azimuth θn is a measurement condition, it is a known number, and the amount of inclination I _φ and the inclination azimuth angle θ _φ are unknowns A and B, and secondary processing data C ″ n is estimated from arbitrary A and B.

A ratio Rn between the estimated secondary machining data C ″ n and the measured secondary machining data Dn ″ is obtained.

When the unknown B is adjusted in an arbitrary range and B becomes equal to the tilt azimuth (B = θφ), the following equation is established, and this ratio at each measurement azimuth becomes a constant value.

Using this, the variance sigma _R ratio Rn at each measuring azimuth θn of secondary processing data calculated for any B, and B _ml of the dispersion sigma _R becomes minimum, the tilt direction angle theta _phi Maximum likelihood value.

From this, the amount of inclination _Iφ is calculated. The arithmetic mean of the ratio Rn at the maximum likelihood value B _ml of the obtained tilt azimuth angle θ _φ is expressed as follows when the unknown A is 1.

The arithmetic mean of the time of B = B _ml and the maximum likelihood value of the lean amount I _phi. As shown in FIG. 35, when the unknown B is obtained as B _ml that minimizes the variance σ _R in the entire circumference range, two directions of 180 ° azimuth difference are obtained. Accordingly, the interval for calculating the variance σ _R by shifting the unknown B in an arbitrary range is the interval [0 to π], and the maximum likelihood value near the azimuth angle obtained by adding π to the azimuth angle that becomes the maximum likelihood value in this interval. Is calculated. Since the measurement value includes an error, the average of the calculated two tilt azimuths is obtained and set as the azimuth direction. If there is a tilt azimuth angle in these two parallel directions, and the elevation angle direction of the tilt is the tilt azimuth angle direction, the azimuth in which the calculated arithmetic mean of the two tilt directions is in a positive integer section is selected as the tilt azimuth angle. To do.

4.3.6. Processing procedure 6 (calculation of average value)
When each measurement cycle is repeated k = 1, 2,..., K _k times, the measurement values obtained in the measurement cycle k are defined as follows.
In order to improve the measurement accuracy, an average of measured values in all cycles k = 1 to _kk is _obtained .

4.3.7. Processing procedure 7 (Evaluation of temperature dependence)
For each measurement cycle, k = 1, 2,..., The average of the temperature sensor outputs Tm in the measurement interval of the cycle is calculated, and Tm is set as the measurement temperature in the cycle interval. The measured temperature average value Tk of k cycles is as follows.

From the correlation between the average temperature Tk of each measurement cycle k and the measured value _DFk of the static error, the temperature dependence of the static error _DFk is evaluated as shown in FIG. The correlation shown in FIG. 36 can be approximated by a polynomial of a quadratic function or more (h ≧ 2) having a temperature characteristic correction coefficient for each term as follows.

4.3.8. Processing procedure 8 (correction for measurement results)
The input / output of the acceleration sensor can be defined as follows to make corrections.

The bias correction can be performed by defining the input / output of the acceleration sensor as follows. In order to update the temperature characteristic correlation, temperature characteristic correction is not performed during calibration measurement.

4.3.9. Correction Value Update Processing Next, the correction value update operation according to the above-described processing steps 1 to 7 will be described with reference to FIG. First, with respect to the acceleration sensor, association with the horizontal coordinate system shown in FIG. 4, measurement conditions, and the like are initially set (step 1). As a separate measurement condition, set the measurement conditions, for example, random drift rate D _R as shown in FIG. 26 becomes minimum (step 2), initializes the segment A-B shown in FIG. 26 (Step 3). Thereafter, as shown in FIGS. 27 to 30, the acceleration sensor is sequentially rotated and stopped to perform measurement (step 4). The determination of the definition of one cycle section shown in FIGS. 27 to 30 is performed for each rotation stationary (step 5). If the one-cycle section shown in FIGS. 27 to 30 is not established (NO in step 6), the process returns to step 4. If one cycle section is established (YES in step 6), the process proceeds to step 7. In step 7, primary processing data is generated by subtracting a dynamic error from the output Dm of the acceleration sensor, and an average value of the primary processing data is generated in one cycle section. Further, the secondary machining data is obtained by subtracting the static error from the primary machining data, and various correction values are calculated based on the secondary machining data (step 8). It is determined whether or not the measurement at the rotational stationary position has been completed for all the cycles (step 9). If the determination in step 9 is NO, the process returns to step 4. If the determination in step 9 is YES, step 10 is performed. Migrate to In step 10, for example, an average of measured values in all cycles k = 1 to _kk is obtained as a statistical calculation, and the statistical value is updated as a corrected value (step 11).

4.3.10. Measurement of Inclination Angle, etc. FIG. 38 explains inclinometer measurement operations such as an inclination angle, an inclination azimuth angle, and an inclination amount according to the above-described processing procedures 1-8. In FIG. 38, Step 1 to Step 11 are the same as FIG. 37, and Step 12 is added. In FIG. 38, after the correction value is updated in step 11, it is determined whether or not the inclinometer measurement operation such as the tilt angle, the tilt azimuth angle, and the tilt amount is finished (step 12). If the determination in step 12 is NO, the process returns to step 4 to perform inclinometer measurement operations such as the tilt angle, tilt azimuth, and tilt amount in steps 4 to 11. Here, in the statistical calculation in step 10 of FIG. 38, the average value theta _.phi.R tilt azimuth using the measured data and calibration _values, the inclination amount of the average I _.phi.R, average phi _R tilt angle is determined.

  Although the present embodiment has been described in detail as described above, it will be easily understood by those skilled in the art that many modifications can be made without departing from the novel matters and effects of the present invention. Therefore, all such modifications are included in the scope of the present invention.

  For example, after passing through at least two second stationary positions (for example, 90 degrees, 180 degrees, and 270 degrees) from the first stationary position (for example, 0 degrees) set as the reference direction, the third stationary position (360 degrees) that is the reference direction again. = 0 degrees), the measurement is performed in a plurality of cycles as shown in FIGS. 39 and 40.

  In the example shown in FIG. 39, after rotating counterclockwise from 0 degree → 90 degrees → 180 degrees, it is rotated clockwise from 180 degrees → 90 degrees → 0 degrees and rotating in the opposite direction alternately. ing. This is because internal wiring breaks down when it is continuously rotated in one direction. In the example of FIG. 39, the first direction (0 degrees → 90 degrees → 180 degrees → 0 degrees) and the second cycle (180 degrees → 90 degrees → 0 → 180 degrees) have a reference orientation of 0 degrees, 180 degrees. Each degree is different.

  On the other hand, in the example shown in FIG. 40, after rotating counterclockwise from 0 degrees → 90 degrees → 180 → 270 degrees, it is rotated back to 270 degrees → 0 degrees clockwise. In the example of FIG. 40, the first cycle (0 degree → 90 degrees → 180 degrees → 270 degrees → 0 degree), the second cycle (90 degrees → 180 degrees → 270 degrees → 0 degree → 90 degrees), The third cycle (180 degrees → 270 degrees → 0 degrees → 90 degrees → 180 degrees) and the fourth cycle (270 degrees → 0 degrees → 90 degrees → 180 degrees → 270 degrees) are the reference orientations of 0 degrees and 90 degrees , 180 degrees and 270 degrees.

  FIG. 41 shows an operation flow for collecting data through a waiting time from the measurement start command. After the instruction from the terminal PC2 to the measurement terminal device 3, the measurement terminal device 3 outputs data, but the terminal PC2 does not capture the data. As described above, the waiting time is provided to select a stable time zone in which the environmental temperature fluctuation is small. As shown in FIG. 41, the data taken into the terminal PC after the elapse of the waiting time can be averaged every predetermined cycle to improve the measurement accuracy.

1 host device, 2 terminal device, 3 measurement terminal device, 4 housing, 4A installation surface, 5 rotation operation unit, 6 indicator, 7 communication device, 8 rotation drive unit, 10x, 10y, 10z acceleration sensor, 20 storage device, 30 rotation command unit, 40 error measurement unit, 41 dynamic error measurement unit, 42 static error measurement unit, 43 tilt error measurement unit, 50 tilt degree measurement unit, 51 tilt angle measurement unit, 52 tilt azimuth angle measurement unit, 60 Tilt bias correction unit, 70 communication device, XYZ sensor coordinate system, XrYrZr absolute coordinate system, θ tilt azimuth angle, φ tilt angle, Iφ · cos θ, Iφ · sin θ tilt error, DFx, DFy static error, Dx _ΔT ΔT, Dy _ΔT ΔT Dynamic error, X0, X1, X2,... Y0, Y1, Y2 ... Measurement value, X0, X'1, X'2, ... Y'0, Y'1, Y'2 ... Primary machining data

Claims (14)

A first measurement direction in which one detection axis of the two orthogonal axes of the acceleration sensor having a detection axis of two orthogonal axes in a virtual plane intersecting with the direction of gravity is set as a reference direction, and around a normal to the virtual plane Detection of the two orthogonal axes measured in a stationary state set in each of a second measurement azimuth 180 degrees away from the first measurement azimuth at a rotational position and a third measurement azimuth returned to the reference azimuth. An error measurement step of measuring a different dynamic error in each of the first to third measurement orientations using an output of an acceleration sensor having an axis;
The dynamic error and the substantially constant static error in each of the first to third measurement directions are removed from the output of the acceleration sensor set to the first measurement direction and the second measurement direction. An inclination measuring step for measuring at least one of the inclination angle and the inclination azimuth based on the data depending on the inclination angle and the inclination azimuth angle with which the virtual plane is inclined with respect to the horizontal plane;
Have
The error measurement step includes a step of measuring the dynamic error based on a difference between outputs of the acceleration sensor set in the first measurement direction and the third measurement direction. Method. In the inclination measuring method according to claim 1,
In the inclination measuring step, the orthogonal biaxial detection axes are the X axis and the Y axis, the inclination angle is φ, the inclination azimuth is θ, and the gravity component projected on the virtual plane is Iφ. Then, the X-axis component X ″ ₀ = Iφ (cos θ) and the Y-axis component Y ″ ₀ = Iφ (sin θ) of gravity in the first measurement direction, and the X-axis component X ″ of gravity in the second measurement direction ₁ = −X ″ ₀ and Y component Y ″ ₁ = −Y ″ _0, and the average value X ″ ₀₁ = (X ″) of the X-axis component of gravity in the first measurement orientation and the second measurement orientation ₀₋ X ″ ₁ ) / 2 and the average value Y ″ ₀₁ = (Y ″ ₀ −Y ″ ₁ ) / 2 of the Y-axis component of gravity in the first measurement azimuth and the second measurement azimuth. Then, Iφ = (X ″ ₀₁ ² + Y ″ ₀₁ ² ) ^1/2 is obtained, and the inclination angle φ = 180 × Iφ / π is calculated. In the inclination measuring method according to claim 1,
In the inclination measuring step, the orthogonal biaxial detection axes are the X axis and the Y axis, the inclination angle is φ, the inclination azimuth is θ, and the gravity component projected on the virtual plane is Iφ. Then, the X-axis component X ″ ₀ = Iφ (cos θ) and the Y-axis component Y ″ ₀ = Iφ (sin θ) of gravity in the first measurement direction, and the X-axis component X ″ of gravity in the second measurement direction ₁ = −X ″ ₀ and Y component Y ″ ₁ = −Y ″ ₀ , X-axis component X ″ ₁ = −X ″ ₀ and Y component Y ″ ₁ = −Y ″ _{0 of} the second measurement orientation , And the average value X ″ ₀₁ = (X ″ ₀ −X ″ ₁ ) / 2 of the X-axis component of gravity in the first measurement direction and the second measurement direction, and the first measurement direction and the mean value of the Y-axis component of gravity in the second measurement direction _{Y "01 = (Y" 0} -Y "1) / 2 and by using the ^{_{Iφ = (X" 01 2 +}} Y "01 2 Seeking ^1/2, said X and Y-axis component _{X "0, X" 1,} Y "0, Y" 1 and is divided by Iφ normalized, and measuring the inclination azimuth angle θ Inclination measurement method. One of the orthogonal biaxial detection axes of the acceleration sensor having an orthogonal biaxial detection axis in a virtual plane that intersects the direction of gravity is set to a first measurement direction set as a reference direction, and around a normal to the virtual plane A second measurement orientation 90 degrees away from the first measurement orientation at a rotational position, a third measurement orientation 180 degrees away from the first measurement orientation at a rotational position around the normal, and the normal The orthogonality of the acceleration sensor measured in a stationary state at each of a fourth measurement azimuth 270 degrees away from the first measurement azimuth and a fifth measurement azimuth returned to the reference azimuth at a rotational position around An error measurement step of measuring different dynamic errors in each of the first to fifth measurement orientations using outputs of two detection axes;
The dynamic error and the substantially constant static error in each of the first to fifth measurement directions are removed from the output of the acceleration sensor set to the first to fourth measurement directions, An inclination measurement step for measuring at least one of the inclination angle and the inclination azimuth based on data depending on an inclination angle and an inclination azimuth angle at which the virtual plane is inclined with respect to a horizontal plane;
Have
The error measurement step includes a step of measuring the dynamic error based on a difference between outputs of the acceleration sensor set in the first measurement direction and the fifth measurement direction. Method. In the inclination measuring method according to claim 4,
In the inclination measuring step, the orthogonal biaxial detection axes are the X axis and the Y axis, the inclination angle is φ, the inclination azimuth is θ, and the gravity component projected on the virtual plane is Iφ. Then, the X-axis component X ″ ₀ = Iφ (cos θ) and the Y-axis component Y ″ ₀ = Iφ (sin θ) of gravity in the first measurement direction, and the X-axis component X ₁ of gravity in the second measurement direction = Iφ (sin θ) and Y component Y ₁ = Iφ (cos θ), X component X ″ ₂ = −X ″ ₀ and Y component Y ″ ₂ = −Y ″ ₀ of gravity in the third measurement orientation, The X-axis component X ″ ₃ = −X ″ ₁ and the Y component Y ″ ₃ = −Y ″ ₁ of gravity in the fourth measurement orientation are obtained, and the gravity of the gravity in the first measurement orientation and the third measurement orientation is determined. an X-axis average _{X "03 = (X" 0} -X "3) / 2 or the average value _Y of the Y-axis _{component" 03 = (Y "0 -Y} " 3) components / 2, The average of the X-axis component of the gravitational the serial second measurement direction and at the fourth measurement azimuth value _X "24 _{= (X"} 2 -X _'4) / 2 or the average value _Y of the Y-axis component _"24 = ( Y ″ ₂ −Y ″ ₄ ) / 2 and Iφ = (X ″ ₀₃ ² + X ″ ₂₄ ² ) ^1/2 or Iφ = (Y ″ ₀₃ ² + Y ″ ₂₄ ² ) ^1/2 An inclination measuring method, wherein an angle φ = 180 × Iφ / π is calculated. In the inclination measuring method according to claim 4,
In the inclination measuring step, the orthogonal biaxial detection axes are the X axis and the Y axis, the inclination angle is φ, the inclination azimuth is θ, and the gravity component projected on the virtual plane is Iφ. Then, the X-axis component X ″ ₀ = Iφ (cos θ) and the Y-axis component Y ″ ₀ = Iφ (sin θ) of gravity in the first measurement direction, and the X-axis component X ₁ of gravity in the second measurement direction = Iφ (sin θ) and Y component Y ₁ = Iφ (cos θ), X component X ″ ₂ = −X ″ ₀ and Y component Y ″ ₂ = −Y ″ ₀ of gravity in the third measurement orientation, The X-axis component X ″ ₃ = −X ″ ₁ and the Y component Y ″ ₃ = −Y ″ ₁ of gravity in the fourth measurement orientation are obtained, and the gravity of the gravity in the first measurement orientation and the third measurement orientation is determined. an X-axis average _{X "03 = (X" 0} -X "3) / 2 or the average value _Y of the Y-axis _{component" 03 = (Y "0 -Y} " 3) components / 2, The average of the X-axis component of the gravitational the serial second measurement direction and at the fourth measurement azimuth value _X "24 _{= (X"} 2 -X _'4) / 2 or the average value _Y of the Y-axis component _"24 = ( Y ″ ₂ −Y ″ ₄ ) / 2 is used to obtain Iφ = (X ″ ₀₃ ² + X ″ ₂₄ ² ) ^1/2 or Iφ = (Y ″ ₀₃ ² + Y ″ ₂₄ ² ) ^1/2 An inclination measuring method characterized by measuring the inclination azimuth angle θ by normalizing the X and Y axis components X ″ ₀ , X ″ ₁ , Y ″ ₀ , Y ″ ₁ by dividing by Iφ. In claim 3 or 6,
The inclination measuring step is performed by dividing the X and Y axis components X ″ ₀ , X ″ ₁ , Y ″ ₀ , Y ″ ₁ by Iφ and normalizing the X and Y axis components X ′ having an amplitude of ± 1. ″ ₀ , X ′ ″ ₁ , Y ′ ″ ₀ , Y ′ ″ ₁ are converted into Cartesian coordinates of the Gaussian plane, and the tilt azimuth angle θ is in any of the first to fourth quadrants of the Gaussian plane. A method for measuring the degree of inclination, comprising the step of determining whether or not the slope exists. In the inclination measuring method according to any one of claims 1 to 7,
When the measurement until the detection axis is rotated from the reference azimuth and returned to the reference azimuth is 1 cycle, when the cycle number n is 2 or more, the measurement is performed over n cycles, and the nth cycle The first measurement direction is also used as the measurement direction of the (n-1) th cycle. In the inclination measuring method according to any one of claims 1 to 8,
The detection axis of the acceleration sensor is rotated in a first direction from the reference azimuth, and then rotated in a second direction opposite to the first direction toward the reference azimuth. Inclination measurement method. One of the orthogonal biaxial detection axes of the acceleration sensor having an orthogonal biaxial detection axis in a virtual plane that intersects the direction of gravity is set to a first measurement direction set as a reference direction, and around a normal to the virtual plane Means for outputting a command to set each of the second measurement azimuth 180 degrees away from the first measurement azimuth at the rotational position and the third measurement azimuth returned to the reference azimuth;
Means for receiving an output of the acceleration sensor set in each of the first to third measurement directions;
Error measurement means for measuring different dynamic errors in each of the first to third measurement orientations using the output of the acceleration sensor;
From the output of the acceleration sensor set to the measurement direction of each of the first measurement direction and the second measurement direction, the dynamic error is substantially constant in each of the first to third measurement directions. Means for measuring at least one of the tilt angle and the tilt azimuth angle based on data depending on a tilt angle and a tilt azimuth angle at which the virtual plane is tilted with respect to a horizontal plane, from which static errors have been removed;
Have
The inclination measuring device, wherein the error measuring means measures the dynamic error based on a difference between outputs of the acceleration sensor set in the first measurement direction and the third measurement direction. One of the orthogonal biaxial detection axes of the acceleration sensor having an orthogonal biaxial detection axis in a virtual plane that intersects the direction of gravity is set to a first measurement direction set as a reference direction, and around a normal to the virtual plane A second measurement orientation 90 degrees away from the first measurement orientation at a rotational position, a third measurement orientation 180 degrees away from the first measurement orientation at a rotational position around the normal, and the normal Means for outputting a command to be set for each of a fourth measurement azimuth 270 degrees away from the first measurement azimuth at a rotational position around and a fifth measurement azimuth returned to the reference azimuth;
Means for receiving an output of the acceleration sensor set in each of the first to fifth measurement directions;
Error measurement means for measuring different dynamic errors in each of the first to fifth measurement orientations using the output of the acceleration sensor;
From the output of the acceleration sensor set to the measurement direction of each of the first to fourth measurement directions, the dynamic error and a static error that is substantially constant in each of the first to fifth measurement directions. Means for measuring at least one of the tilt angle and the tilt azimuth angle based on data depending on the tilt angle and tilt azimuth angle at which the virtual plane is tilted with respect to the horizontal plane.
Have
The inclination measuring device, wherein the error measuring means measures the dynamic error based on a difference between outputs of the acceleration sensors set in the first measurement direction and the fifth measurement direction.   An electronic apparatus comprising the inclination measuring device according to claim 10. One of the orthogonal biaxial detection axes of the acceleration sensor having an orthogonal biaxial detection axis in a virtual plane that intersects the direction of gravity is set to a first measurement direction set as a reference direction, and around a normal to the virtual plane Outputting a command to set each of the second measurement azimuth 180 degrees away from the first measurement azimuth at the rotational position and the third measurement azimuth returned to the reference azimuth;
Receiving an output from the acceleration sensor set in the first to third measurement directions;
A procedure for measuring different dynamic errors in each of the first to third measurement orientations using the output of the acceleration sensor measured in a stationary state in each of the first to third measurement orientations;
From the output of the acceleration sensor set to each of the first measurement direction and the second measurement direction, the dynamic error and the static error that is substantially constant in each of the first to third measurement directions. Measuring at least one of the tilt angle and the tilt azimuth angle based on data depending on a tilt angle and a tilt azimuth angle at which the virtual plane is tilted with respect to a horizontal plane from which an error is removed;
To the computer,
The procedure for measuring the dynamic error includes a procedure for measuring the dynamic error based on a difference between outputs of the acceleration sensor in the first measurement direction and the third measurement direction. . One of the orthogonal biaxial detection axes of the acceleration sensor having an orthogonal biaxial detection axis in a virtual plane that intersects the direction of gravity is set to a first measurement direction set as a reference direction, and around a normal to the virtual plane A second measurement orientation 90 degrees away from the first measurement orientation at a rotational position; a third measurement orientation 180 degrees away from the first measurement orientation at a rotational position around a normal to the virtual plane; A procedure for outputting a command to be set for each of the fourth measurement azimuth 270 degrees away from the first measurement azimuth at the rotational position around the normal to the virtual plane and the fifth measurement azimuth returned to the reference azimuth. When,
Receiving an output from the acceleration sensor set in the first to fifth measurement directions;
A procedure for measuring different dynamic errors in each of the first to fifth measurement orientations using the output of the acceleration sensor measured in a stationary state in each of the first to fifth measurement orientations;
From the output of the acceleration sensor set to the measurement direction of each of the first to fourth measurement directions, the dynamic error and a substantially constant static error in each of the first to fifth measurement directions Measuring at least one of the tilt angle and the tilt azimuth angle based on data depending on the tilt angle and tilt azimuth angle at which the virtual plane is tilted with respect to the horizontal plane,
To the computer,
The procedure for measuring the dynamic error includes a procedure for measuring the dynamic error based on a difference between outputs of the acceleration sensor in the first measurement direction and the fifth measurement direction. .