Offset derivation device, offset calculation device, and azimuth sensor

An offset derivation device that derives an offset value for generating corrected magnetism detection data by correcting original magnetism detection data acquired sequentially as data points in a three- or two-axis coordinate system through sensing of magnetism along three or two axes, the device comprising:

• a tentative value deriver configured to calculate a tentative value of the offset value by using a plurality of data points in the original or corrected magnetism detection data;
• and
• an updater configured to derive magnitude of the magnetism based on the original magnetism detection data and the tentative value, the updater being configured, if the derived magnitude of the magnetism is within a predetermined reference range, to update the offset value with the tentative value and otherwise to keep the offset value unupdated, wherein
• the tentative value deriver is configured
• to take one of the plurality of data points, which comprise N data points (where N is an integer of 2 or more), as a reference data point, and translate uniformly the plurality of data points such that the reference data point coincides with an origin of the three- or two-axis coordinate system, thereby to set (N−1) imaginary data points except for the reference data point, and then
• to derive, as an imaginary offset point, either a point that is located at a center of a curved surface passing through the origin O of the three-axis coordinate system and that minimizes a sum of distances from the curved surface to the respective imaginary data points or a point that is located at a center of a curved line passing through the origin O of the two-axis coordinate system and that minimizes a sum of distances from the curved line to the respective imaginary data points, and translate the imaginary offset point such that previously done translation is undone, thereby to derive the tentative value, wherein
• when, in the two-axis coordinate system, coordinate values of an ith imaginary data point among the (N−1) imaginary data points are represented by (Hxi′, Hyi′) (where i is an integer of 1 or more but (N−1) or less) and coordinate values of the imaginary offset point are represented by (Hx0′, Hy0′), the tentative value deriver derives the coordinate values of the imaginary offset value so as to minimize a value of a function FH2 given by formula (A2) below:
• [
• Formula
• ⁢
• ⁢
• 2
• ]
• F
• H
• ⁢
• ⁢
• 2
• =
• ∑
• i
• =
• 1
• N
• -
• 1
• ⁢
• ⁢
• (
• Hxi
• ′2
• +
• Hyi
• ′2
• -
• 2
• ⁢
• Hxi
• ′
• ·
• Hx
• ⁢
• ⁢
• 0
• ′
• -
• 2
• ⁢
• Hyi
• ′
• ·
• Hy
• ⁢
• ⁢
• 0
• ′
• )
• 2
• .
• (
• A2
• )

An offset calculation device configured

• to refer to three-axis magnetism detection data acquired sequentially as data points in a three-axis coordinate space, thereby to continually search for six data points (Hxi, Hyi, Hzi) (where i=1 to 6) corresponding to maximum values and minimum values for individual axes respectively;
• to determine a seventh reference data point (Hx7, Hy7, Hz7) when differences between the maximum and minimum values for the individual axes respectively are all larger than a threshold value;
• to translate uniformly, of the six data points, at least four points corresponding respectively to the maximum and minimum values for X and Y axes such that the reference data point coincides with an origin (0, 0, 0) while ignoring coordinate values for a Z axis, thereby to calculate imaginary data points (Hxi′, Hyi′) (where i=1 to 4) on an XY coordinate plane;
• to calculate an imaginary offset point (Hx0′, Hy0′) on the XY coordinate plane that minimizes a function F1 given by formula (f1) below by using the imaginary data points (Hxi′, Hyi′);
• F1=Σi(Hxi′2+2Hyi′2−2Hxi′·Hx0′−2Hyi′·Hy0′)2 (f1)
• to translate the imaginary offset point (Hx0′, Hy0′) such that previously done translation of the reference data point is undone, thereby to calculate offset values Hx0 and Hy0 for the X and Y axes;
• to translate uniformly the six data points such that the reference data point coincides with the origin, thereby to calculate six imaginary data points (Hxi′, Hyi′, Hzi′) (where i=1 to 6);
• to calculate an imaginary offset value Hz0′ that minimizes a function F2 given by formula (f2) below by using the imaginary offset point (Hx0′, Hy0′) and the six imaginary data points (Hxi′, Hyi′, Hzi′);
• and
• F2=Σi(Hxi′2+Hyi′2+Hzi′2−2Hxi′·Hx0′−2Hyi′·Hy0′−2Hzi′·Hz0′)2 (f2)
• to translate the imaginary offset value Hz0′ such that previously done translation of the reference data point is undone, thereby to calculate an offset value Hz0 for the Z axis.

An offset calculation device configured

• to refer to three-axis magnetism detection data acquired sequentially as data points in a three-axis coordinate space, thereby to continually search for six data points (Hxi, Hyi, Hzi) (where i=1 to 6) corresponding to maximum values and minimum values for individual axes respectively;
• to determine a seventh reference data point (Hx7, Hy7, Hz7) when differences between the maximum and minimum values for the individual axes respectively are all larger than a threshold value;
• to calculate offset values Hx0 and Hy0 are calculated for X and Y axes by use of formula (f3a) and (f3b) below.
• Hx
• ⁢
• ⁢
• 0
• =
• Hx
• ⁡
• (
• max
• )
• +
• Hx
• ⁡
• (
• min
• )
• 2
• ,
• (
• f3a
• )
• Hy
• ⁢
• ⁢
• 0
• =
• Hy
• ⁡
• (
• max
• )
• +
• Hy
• ⁡
• (
• min
• )
• 2
• ,
• (
• f3b
• )
• in formula (f3a) and (f3b) above, Hx(max) and Hx(min) representing maximum value and minimum value for the X axis, and Hy(max) and Hy(min) representing maximum value and minimum value for the Y axis,
• to translate uniformly the six data points such that the reference data point coincides with the origin, thereby to calculate six imaginary data points (Hxi′, Hyi′, Hzi′) (where i=1 to 6);
• to calculate an imaginary offset value Hz0′ that minimizes a function F2 given by formula (f2) below by using the imaginary offset point (Hx0′, Hy0′) and the six imaginary data points (Hxi′, Hyi′, Hzi′);
• and
• F2=Σi(Hxi′2+Hyi′2+Hzi′2−2Hxi′·Hx0′−2Hyi′·Hy0′−2Hzi′·Hz0′)2 (f2)
• to translate the imaginary offset value Hz0′ such that previously done translation of the reference data point is undone, thereby to calculate an offset value Hz0 for a Z axis.