WO2008122905A1

WO2008122905A1 - Sensor compensation in orientation sensing system

Info

Publication number: WO2008122905A1
Application number: PCT/IB2008/051150
Authority: WO
Inventors: Hans Marc Bert Boeve; Teunis Jan Ikkink
Original assignee: Nxp B.V.
Priority date: 2007-04-04
Filing date: 2008-03-27
Publication date: 2008-10-16
Also published as: TW200907300A

Abstract

An apparatus is configured for measuring the 3D earth-magnetic field at the geographic location of the apparatus. The apparatus has a 2D sensor arrangement. A 2x3 matrix maps the magnetic vector's components to the sensor outputs. A coordinate system is determined so that the 2x3 matrix transformed to this coordinate system has a column with only zeros. This enables to invert the matrix and to obtain two of the three vector components. The third component is determined using a predetermined constraint imposed on the magnetic vector.

Description

Sensor compensation in orientation sensing system

FIELD OF THE INVENTION

The invention relates to an electronic apparatus for measuring a three-dimensional vector representative of a three-dimensional vector field at a geographic location of the apparatus. The invention further relates to a method of measuring a three-dimensional vector representative of a three-dimensional vector field at a geographic location

BACKGROUND ART

Magnetometers and accelerometers are used in sensors for orientation sensing systems such as an electronic compass in order to measure the earth-magnetic field and gravity. The earth-magnetic field is a three-dimensional (3D) vector field. The sensor has multiple axes, each of which responds to a particular component of the field to be measured. The response of a particular sensor axis Si to the field of interest U may be modeled by a linear equation in the three components of the field vector U as specified by equation (102) in Fig.l . Equation 102 has four parameters, of which three (SFj_x, SF )_y, SF]₂) represent the sensitivities to the three components of the field vector and the fourth (S )β) describes the sensor's offset. The notation "SF' stands for scale factor. For a 3D sensor, the three scalar equations can be written as a single matrix equation (104), or as equation (106) in vector notation. In the latter, superscript "^τ" denotes the transpose operator: SFi is a column vector, whereas SFi is a row vector. In order to determine the field vector U of interest (e.g., magnetic field, gravity) from the three signals Si, S2 and S3 as measured by the sensor, matrix equation (106) is inverted so as to obtain vector equation (108).

However, if a two-dimensional (2D) sensor is used to measure a 3D vector field, the scale factor matrix is not square. As a result, its inverse does not exist. Accordingly, for a 2D sensor it is not straightforward to determine the 3D field vector starting from the 2D sensor data.

WO2006117731 (attorney docket PH000319), herein incorporated by reference, discloses a device that has a sensor arrangement for providing first field information defining at least parts of a first field and for providing second field information defining first parts of a second field. The device has an estimator for estimating second parts of the second field as functions of mixtures of the first and second field information. The fields may be the earth gravitational field and/or the earth-magnetic field and/or further fields. The mixtures comprise dot products of the first and second fields and/or first products of first components of the first and second fields in first directions and/or second products of second components of the first and second fields in second directions. The second parts of the second field comprise third components of the second field in third directions. The estimator can further estimate third components of the first field in third directions as further functions of the first field information.

WO20061117731 therefore describes a vector reconstruction method for reconstructing a missing component of one or two vector fields, given the other components of the vector fields as measured by a 2D sensor, as well as knowledge of the magnitude of both fields and their dot-product.

SUMMARY OF THE INVENTION

The vector reconstruction method described in WO2006117731 works well to reconstruct the missing component of a vector field, given (e.g. by measurement) the other two components of the vector field. If both axes of the 2D sensor are well aligned to the x-y plane of the body-coordinate system, then the x- and y-components of the vector field can be easily calculated from the sensor signals Si and S₂. This is because a 2D inverse of the scale factor matrix can be readily calculated as given by expressions (202) of Fig.2. The method of WO2006117731 then supplies the third component.

However, in practice the sensor axes are not necessarily well aligned with the x-y plane of the body-coordinate system. This is due to, among other things, mounting tolerances. In the case of a magnetometer, the influence of nearby soft-magnetic materials may change strength and direction of the earth -magnetic field as measured. In this practical case the scale factor matrix has non-zero coefficients in the third column. This signifies that the sensors are sensitive to the z- component of the field as well. As a result, the 2D inverse of the scale factor matrix cannot be determined, and the vector reconstruction as described in WO2006117731 cannot be applied.

It is an object of the present invention to provide a solution for this problem, so that vector reconstruction can still be performed if the axes of the 2D sensor are not well aligned with the x-y plane of the body coordinate system. In the vector reconstruction technique described in WO2006117731 it is assumed that two Cartesian components of the vector to be determined are known (e.g. from measurement) and the third Cartesian component is reconstructed given a value for either the magnitude of the vector or the dot-product of the vector field with another, known (or measured) vector field. If a row in the scale factor matrix has non-zero off-diagonal coefficients, the sensitivity axis of the corresponding sensor (i.e., the direction for which the sensor is sensitive) is not aligned with the respective axis of the body-coordinate system. The direction of the row vector in the scale factor matrix is representative of the sensitivity axis. The two sensitivity axes of a 2D sensor together thus span up a 2D plane in the 3D body-coordinate system. The invention now uses a new Cartesian coordinate system having orthogonal base vectors p, q, and r of unit length, with two of its three base vectors, e.g., p, q, lying in the plane spanned by the sensitivity vectors of the 2D sensor. After defining the (p, q, r) coordinate system, both sensitivity axes can be expressed entirely in terms of the p- and q- base vectors. Hence the p- and q-components of the vector field can be determined in a simple manner from the 2D sensor data by a 2D inverse matrix equation. With the p- and q- components of the vector field known, vector reconstruction as described in WO2006117731 can now be applied to calculate the missing r-component of the vector field. If the vector reconstruction technique relies on the constant dot-product of the field, to be determined, with another field, then first a coordinate transformation is applied to the other field in order to obtain its representation in the (p, q, r) coordinate system. After reconstruction, a coordinate transformation is applied to the reconstructed vector in order to obtain its equivalent representation in terms of the body-coordinate system.

Therefore, the invention relates to an apparatus configured for determining a three-dimensional vector representative of a three-dimensional vector field at a geographic location of the apparatus. The apparatus has a sensor arrangement operative to provide first and second sensor values representative of first and second linear combinations, respectively, of components of the vector with respect to a three-dimensional coordinate system. The apparatus has data processing means connected to the sensor arrangement. The data processing means is operative to express first and second components of the vector, with respect to another three- dimensional coordinate system, as first and second further linear combinations, respectively, of the first and second sensor values, and to determine a third component of the vector, with respect - A - to the other coordinate system, based on a predetermined constraint imposed on the vector.

Accordingly, by means of properly transforming the measurements to a new coordinate system, the inverse of the matrix exists whereupon the missing vector component can be determined through an additional constraint.

The predetermined constraint refers to, e.g., a predetermined magnitude of the vector or a predetermined value of a dot product of the vector with further vector representative of another vector field. If the vector first-mentioned is a vector of the earth-magnetic field, then the vector's magnitude can be considered constant in a particular geographic area for the practical purposes of the invention, and can therefore be used to determine the orientation of the apparatus with respect to the earth-magnetic field. If the further vector is representative of the earth's gravity field, similar considerations apply as gravity can be considered as having a constant magnitude and direction within a particular geographic area for the practical purposes of the apparatus in the invention.

Accordingly, the invention provides an apparatus for determining the 3D earth- magnetic field at the geographic location of the apparatus. This can be used as orientation information by the user of the apparatus. The apparatus has a 2D sensor arrangement. A 2x3 matrix maps the magnetic vector's components to the sensor outputs. A coordinate system is determined so that the 2x3 matrix, transformed to this coordinate system, has a column with only zeros. This enables inversion of the matrix and obtaining two of the three vector components. The third component is determined using a predetermined constraint imposed on the magnetic vector.

The method also relates to a method of determining a three-dimensional vector representative of a three-dimensional vector field at a geographic location. The method comprises receiving from a sensor arrangement first and second sensor values representative of first and second linear combinations, respectively, of components of the vector with respect to a three- dimensional coordinate system; expressing first and second ones of the components of the vector, with respect to another three-dimensional coordinate system, as first and second further linear combinations, respectively, of the first and second sensor values, and determining a third component of the vector, with respect to the other coordinate system, based on a predetermined constraint imposed on the vector. The method is relevant to a service wherein, for example, the sensor arrangement and a graphical user interface are accommodated in a mobile device, and the data processing means is located at a server elsewhere. The mobile device communicates with the server via a data network, e.g., the Internet. The three-dimensional vector field is, e.g., the earth- magnetic field. The service provides orientation information to the user of the mobile device on the basis of the device's sensor data and calibration data submitted to the server. As a result, this service can be used to add value to conventional data network services, e.g., mobile telephony. As the creation of the actual orientation information is under control of the server, an additional subscription fee could be requested of the subscriber to the mobile telephony server. Note that the actual sensor data sensed at the same geographic location may differ per mobile device, e.g., owing to the type, alignment and accommodation of the sensor arrangement in the device.

BRIEF DESCRIPTION OF THE DRAWING

The invention is explained in further detail, by way of example and with reference to the accompanying drawing, wherein:

Figs.1-7 give formulae to explain the operations in the invention; and

Figs.8-10 are block diagrams of apparatus in the invention.

Throughout the Figures, similar or corresponding features are indicated by same reference numerals.

DETAILED EMBODIMENTS

As already discussed above, determining the x-component and the y-component of a 3D vector, based on data provided by a 2D sensor by means of simply inverting the sensor matrix equation, requires that the sensor axes be aligned with the x-y plane of the body coordinate system. That is, the 2D sensor needs to have its sensitivity axes aligned in such a manner that the responses registered are only due to the x-component and the y-component of the vector field to be measured, and that the responses do not contain a noticeable contribution from the z-component in the direction perpendicular to the x-y plane. If this is not the case, the sensor matrix equation cannot be inverted and, consequently, the vector reconstruction of WO2006117731 cannot readily be applied. Equation 204 illustrates this case, wherein the 3D vector U cannot be determined using a 2D sensor whose responses are linear combinations of all three components of vector U. The inventors now propose to subject the vector field to be measured to a coordinate transformation so as to express the sensor responses as comprising only contributions from two components of the vector in a new Cartesian coordinate system. Below, several embodiments are discussed illustrating different manners for how to construct the new coordinate system.

A first embodiment uses the two 3D row vectors SFi^T and SF₂ ^1" of equation 204 to define a new Cartesian coordinate system (p, q, r) using the well-known Gram-Schmidt orthonormalization procedure. There are infinitely many choices for a (p, q, r) basis whose p- and q-base vectors have to be in a given plane, here the plane spanned up by the sensitivity axes of the 2D sensor. The only unique base vector (apart from a polarity sign) is the r-base vector which is perpendicular to the given plane and is defined according to formula (302) defining vector r as the vector parallel to the cross-product of column vectors SFi and SF₂ and scaled to unity length. The p-base vector is taken to be parallel to the first sensitivity axis SFi and normalized to unity length according to equation (304). The base vector q is then taken as the cross-product of the r base vector and the p base vector according to equation (306). With the base vectors defined (in terms of the sensitivity vectors, which in turn are represented in the body-coordinate system), the relationship between the 2D sensor signals and the p- and q- components of the vector field U can now be defined. The coefficients of the new scale factor matrix are the projections of the sensitivity vectors onto the p- and q- base vectors as shown in equation (308). Substituting equations (302)-(306) into equation (308) gives equation (402). The matrix in equation (402) can be simplified. The first coefficient in the second column is identical to zero, as the dot product of a vector with another vector that is perpendicular to it is identical to zero. The second coefficient of the second column can be simplified using basic vector identities (404) and (406), leading to equation (408). The first two components of the vector U as expressed on the basis (p, q, r), U_p and U_q, can now readily be obtained by inverting the matrix in equation (408), leading to equation (502). Next, vector reconstruction can be applied, as described in WO2006117731, to calculate the missing field component U_r. This latter component is then determined according to equation (504), based on the premise that the magnitude of vector U is known, or according to equation (506), based on the premise that the dot-product of vector U with a known vector V is known. For the latter reconstruction, a representation of the other vector V in the (p, q, r) coordinate system is needed. Such a representation can be found by applying a

3D matrix rotation (508) to the representation of the vector V in the body coordinate system (x, y, z). As a last step the reconstructed U vector has to be represented in the body coordinate system. This is accomplished by another 3D rotation operation given by equation (510). Accordingly, the above describes a possible vector reconstruction procedure for a 2D sensor whose sensitivity vectors are not adequately aligned with the x-y plane of the body coordinate system of the apparatus accommodating the sensor.

A second embodiment of constructing a new coordinate system uses Singular- Value-Decomposition (SVD) of the matrix in equation (204). SVD is a standard numerical matrix decomposition procedure that is used to decompose the 3x2 transpose scale factor matrix into the form given by equation (602). Herein, R is a unitary 3x3 matrix, W is a diagonal 3x2 matrix (its last row is all-zero), and Z is a unitary 2x2 matrix. A unitary matrix is a matrix whose columns (and rows) are mutually orthogonal vectors of unity length. The columns of the matrix R are the (p, q, r) base vectors of the new coordinate system. Therefore, vector U can be expressed as given in equation (604). Substituting equations (602) and (604) into equation (204) leads to equation (606). The last column of the diagonal matrix W is all-zero, as a result of which that column can be dropped, as well as the associated U_r component, so that a 2D matrix equation (608) is obtained. Note that equation (608) has the same format as equation (408) in the procedure discussed under the first embodiment above, based on the Gram-Schmidt approach. Equation (608) can be inverted to express the field components U_p and U_q in terms of the sensor signals Si and S 2 as given in equation (702). Note that the inverse of a unitary matrix is equal to its transpose, that a diagonal matrix is invariant under a transpose operator, and that the inverse of a diagonal matrix is another diagonal matrix whose diagonal coefficients are the reciprocal of the corresponding diagonal coefficients of the former diagonal matrix. The vector reconstruction and coordinate transformation can be executed in the same way as discussed in the Gram-Schmidt embodiment.

A third embodiment is based on the following premises: the 3D vector U is measured using a 2D sensor; the value of the dot-product of vector U with another 3D vector V is known; vector V has a known magnitude; vector V is determined using a 2D sensor too. If the U- vector is reconstructed using the known dot-product of the U vector and the V vector, the V vector is to be reconstructed first, since the V vector is needed to reconstruct the U vector, as described under the Gram-Schmidt embodiment discussed above. Vector V itself can be reconstructed based on the known magnitude of the V vector, see the discussion of the Gram- Schmidt embodiment above. However, this can be done in neither the body-coordinate system (x, y, z), nor in the (p, q, r) coordinate system of the sensor for the U vector. Instead, another new (p', q', r') coordinate system is needed, that is now associated with the 2D sensor for the V vector. The order of operations is as follows.

The components V_P' and V_q' are determined from the sensor signals Sv₁ and Sv2 using the 2D inverse matrix equation for the V sensor corresponding to equation (502) for the sensor of vector U. Component V_r' is reconstructed using the known magnitude ||V|| of vector V, in a manner similar to how equation (504) was applied to solve for the component U_r, given the magnitude ||U|| of vector U. Then, the reconstructed vector V is represented in the body- coordinate system (x, y, z) in a manner similar to how equation (510) does this for vector U. Next, the reconstructed vector V is represented in the (p, q, r) coordinate system belonging to the U sensor according to equation (508). Further, components U_p and U_q are determined from the sensor signals Su₁ and Su2 using the 2D inverse matrix equation for the 2D U sensor (502). Then, component U_r is determined using the known dot-product U V according to equation (506). Finally, the reconstructed vector U is represented in the body coordinate system (x, y, z) according to equation (510).

Fig.8 is a block diagram of an apparatus 800 in the invention. Apparatus 800 is configured for measuring a three-dimensional vector U representative of a three-dimensional vector field at a geographic location of apparatus 800. For example, vector U is the vector of the earth-magnetic field at the location of apparatus 800. Apparatus 800 has a sensor arrangement 802 operative to provide first and second sensor values (204) representative of first and second linear combinations, respectively, of components of vector U with respect to a three-dimensional coordinate system that can be thought of as being fixed to the body of apparatus 800. Apparatus 800 further has data processing means 804 connected to sensor arrangement 802. Data processing means 804 is operative to express (502; 702) first and second components of vector U, with respect to another three-dimensional coordinate system, as first and second further linear combinations, respectively, of the first and second sensor values, and to determine a third component of vector U, with respect to the other coordinate system, based on a predetermined constraint (504) imposed on vector U. Apparatus 800 also comprises control means 806, e.g., a graphical user interface (GUI) to render a representation of vector U thus determined, or a control module to control a system (not shown) in response to the momentary vector U thus determined, etc. Practical implementations of the invention include an electronic compass, possibly tilt- compensated, and an orientation sensing system that relies on a single 2D magnetometer sensor for the earth-magnetic field. Such an orientation sensing system could be a stand-alone device or accommodated in, e.g. mobile terminals, wristwatches, car-keys, etc. Data processing means 804 and 806 may be combined using same circuitry, e.g., a general purpose data processor or microcontroller.

Fig.9 is a block diagram of a second apparatus 900 in the invention. Apparatus 900 has now, in addition to sensor arrangement 802 also a further sensor arrangement 902. Sensor arrangement 802 is a 2D sensor. Sensor arrangement 802 operates as discussed with reference to Fig.8. Further sensor arrangement 902 is either a 2D sensor or a 3D sensor.

If sensor arrangement 902 is a 2D sensor, it is operative to provide third and fourth sensor values representative of third and fourth linear combinations, respectively, of components of a further vector with respect to the three-dimensional coordinate system. The vector U sensed by sensor arrangement 802 is e.g., the earth-magnetic field, whereas the further vector V is, e.g., the vector of the gravity field at the location of apparatus 900. First, reconstruction of gravity vector V can be performed, using a constraint involving the known magnitude of gravity vector V, in a way similar to expression (504) for earth-magnetic field vector U. Second, earth-magnetic field vector U can be reconstructed using formula (506), indicating that the value of the dot product of the earth-magnetic field vector U with gravity vector V has a known value in a geographic region of use of apparatus 900. Once vectors U and V have been reconstructed, the orientation of apparatus 900 can be determined from these vectors. Operation of apparatus 900 is according to the discussion above of the third embodiment.

If sensor arrangement 902 is a 3D sensor, all three components of gravity vector V can be readily determined from the three sensor values in a manner similar to how expression (108) does this for vector U, and reconstruction of gravity vector V is not needed and predetermined constraint (506) can be used directly for reconstructing vector U. Fig.lO illustrates another embodiment 1000 of the invention. Embodiment 1000 has distributed the entities, addressed in the description of embodiment 800, between a mobile system 1002 and a server 1004, wherein mobile system 1002 and server 1004 communicate via a data network 1006. Embodiment 1000 relates to a method of determining a three-dimensional vector representative of a three-dimensional vector field, e.g., the earth-magnetic field, at a geographic location of mobile system 1002. Server 1004 comprises data processing means 804 discussed supra. The method comprises receiving at server 1004 from sensor arrangement 802 first and second sensor values representative of first and second linear combinations, respectively, of components of the vector with respect to a three-dimensional coordinate system. The method also comprises receiving calibration data, including the scale factor matrix and the offset vector as defined in equations (102) and (104), that are specific per individual sensor arrangement 802. The method further comprises expressing at server 1004 first and second ones of the components of the vector, with respect to another three-dimensional coordinate system, as first and second further linear combinations, respectively, of the first and second sensor values, and determining a third component of the vector, with respect to the other coordinate system, based on a predetermined constraint imposed on the vector. The distributed approach of embodiment 1000 is also applicable to embodiment 900. Mobile system 1002 then accommodates additionally further sensor arrangement 902 that submits its sensor data to data processing means 804 via Internet 1006.

Data processing means 804 introduced above can be implemented using, for example, a generic data processor under control of specific software, a dedicated microcontroller, specific electronic circuitry such as a gate array, etc.

Claims

1. An apparatus (800) configured for determining a three-dimensional vector representative of a three-dimensional vector field at a geographic location of the apparatus, wherein: the apparatus has a sensor arrangement (802) operative to provide first and second sensor values (204) representative of first and second linear combinations, respectively, of components of the vector with respect to a three-dimensional coordinate system; and the apparatus has data processing means (804) connected to the sensor arrangement; the data processing means is operative to express (502; 702) first and second ones of the components of the vector, with respect to another three-dimensional coordinate system, as first and second further linear combinations, respectively, of the first and second sensor values, and to determine a third component of the vector, with respect to the other coordinate system, based on a predetermined constraint (504; 506) imposed on the vector.

2. The apparatus of claim 1, wherein the predetermined constraint (504) comprises a predetermined magnitude of the vector.

3. The apparatus of claim 1, wherein the predetermined constraint (506) comprises a predetermined value of a dot product of the vector with a further vector representative of a further vector field.

4. The apparatus of claim 3, wherein: the apparatus comprises a further sensor arrangement (902) operative to provide third and fourth sensor values representative of third and fourth linear combinations, respectively, of components of the further vector with respect to the three-dimensional coordinate system; the further sensor arrangement is connected to the data processing means; and the data processing means is operative to express (502; 702) first and second ones of the components of the further vector, with respect to a further three-dimensional coordinate system, as third and fourth further linear combinations, respectively, of the third and fourth sensor values, and to determine a third component of the further vector, with respect to the further coordinate system, based on a predetermined magnitude of the further vector.

5. The apparatus of claim 3, wherein: the apparatus comprises a further sensor arrangement (902) operative to provide third, fourth and fifth sensor values representative of third, fourth and fifth linear combinations, respectively, of components of the further vector with respect to the three-dimensional coordinate system; the further sensor arrangement is connected to the data processing means; the data processing means is operative to express (108, 508) first, second and third ones of the components of the further vector, with respect to a further three-dimensional coordinate system, as third, fourth and fifth further linear combinations, respectively, of the third, fourth and fifth sensor values.

6. The apparatus of claim 1, 2, 3, 4 or 5, wherein the three-dimensional vector field is the earth-magnetic field.

7. The apparatus of claim 3, 4 or 5, wherein the three-dimensional vector field is the earth-magnetic field, and wherein the further vector field is the earth's gravity field.

8. The apparatus of claim 1, wherein: the first and second linear combinations are determined by a 2x3 matrix; and the data processing means is operative to determine an orthogonal basis for the other coordinate system by applying a Gram-Schmidt process (302, 304, 306) to the row vectors of the 2x3 matrix.

9. The apparatus of claim 1, wherein: the first and second linear combinations are determined by a 2x3 matrix; and the data processing means is operative to determine an orthogonal basis for the other coordinate system by carrying out a Singular Value Decomposition (602, 604) of a matrix whose transpose is the 2x3 matrix.

10. A method of determining a three-dimensional vector representative of a three- dimensional vector field at a geographic location, wherein the method comprises: receiving via a data network (1006) from a sensor arrangement (802) first and second sensor values (204) representative of first and second linear combinations, respectively, of components of the vector with respect to a three-dimensional coordinate system; and expressing (502; 702) first and second ones of the components of the vector, with respect to another three-dimensional coordinate system, as first and second further linear combinations, respectively, of the first and second sensor values, and to determine a third component of the vector, with respect to the other coordinate system, based on a predetermined constraint (504; 506) imposed on the vector.

11. The method of claim 10, comprising further receiving data representative of calibration information about the sensor arrangement.

12. The method of claim 10, wherein the predetermined constraint (504) comprises a predetermined magnitude of the vector.

13. The method of claim 10, wherein the predetermined constraint (506) comprises a predetermined value of a dot product of the vector with a further vector representative of a further vector field.

14. The method of claim 13, comprising: receiving third and fourth sensor values representative of third and fourth linear combinations, respectively, of components of the further vector with respect to the three- dimensional coordinate system; and expressing (502; 702) first and second ones of the components of the further vector, with respect to a further three-dimensional coordinate system, as third and fourth further linear combinations, respectively, of the third and fourth sensor values, and determining a third component of the further vector, with respect to the further coordinate system, based on a predetermined magnitude of the further vector.

15. The method of claim 13, comprising: receiving third, fourth and fifth sensor values representative of third, fourth and fifth linear combinations, respectively, of components of the further vector with respect to the three-dimensional coordinate system; and expressing (108, 508) first, second and third ones of the components of the further vector, with respect to a further three-dimensional coordinate system, as third, fourth and fifth further linear combinations, respectively, of the third, fourth and fifth sensor values.

16. The method of claim 10, 11, 12, 13, 14 or 15, wherein the three-dimensional vector field is the earth-magnetic field.

17. The apparatus of claim 13, 14 or 15, wherein the three-dimensional vector field is the earth-magnetic field, and wherein the further vector field is the earth's gravity field.