EP2102590A1

EP2102590A1 - A device for and a method of determining the orientation of a plane in space

Info

Publication number: EP2102590A1
Application number: EP07857024A
Authority: EP
Inventors: Fritz K. Brunner; Fritz Zobl; Andreas Wieser
Original assignee: Technische Universitaet Graz; Forschungsholding TU Graz GmbH
Current assignee: Technische Universitaet Graz; Forschungsholding TU Graz GmbH
Priority date: 2006-12-22
Filing date: 2007-12-20
Publication date: 2009-09-23
Also published as: WO2008077595A1

Abstract

A device, a method, a computer program and a computer readable medium for determining an angular orientation of a plane in space is provided, comprising a first unit adapted to receive a first data set indicative of a first physical parameter, and a second unit adapted to receive a second data set indicative of a second physical parameter. Further the device comprises a calculation unit adapted to calculate a transformation array for a transformation based on the first data set, a transformation unit adapted to transform the second data set by using the transformation array, and a determination unit adapted to determine a first angle indicative of an angular orientation of the object in space based on the transformed second data set.

Description

A DEVICE FOR AND A METHOD OF DETERMINING THE ORIENTATION OF A PLANE IN SPACE

FIELD OF THE INVENTION

The invention relates to a device for determining the orientation of a plane in space.

Beyond this, the invention relates to a method of determining the orientation of a plane in space.

Moreover, the invention relates to a geological compass for determining the orientation of a plane in space, in particular of a geological surface.

Furthermore, the invention relates to a computer-readable medium. Beyond this, the invention relates to a program element.

BACKGROUND OF THE INVENTION

The study of three-dimensional (3-D) structures and regions is essential for investigating a geological environment, estimating the tectonic history, and assessing deformation processes. The key data for studies in structural geology as well as in engineering geology are the dip angle (θ) and the dip azimuth (α) of geological features. Numerical values of these measures are derived from field-measurements using a so-called geological compass (GC) which is still the fundamental instrument used in geological field work.

In order to determine the 3-D orientation of a geological feature, the small swivelling test plate of the geological compass needs to be attached to the feature while at the same time the magnetic compass needs to be levelled. Accurate levelling is crucial but can render it very difficult to handle a geological compass properly in certain situations. Taking measurements usually requires both hands of the geologist. A schematic illustration of such a known geological compass is depicted in Fig. 6. The shown geological compass 600 comprises a main body 601 having a compass 602 implemented therein. Further, the geological compass 600 comprises a Bull's eye level 603 in order to indicate whether the geological compass 600 is levelled or not, and a test plate 604 which can be swivelled and is used to be abutted on a geological feature which is schematically shown in Fig. 6 and labelled 605. Furthermore, the geological compass 600 comprises a scale 606 interacting with the test plate 604 in order to determine the dip angle, i.e. the inclination with respect to the gravity field.

The precision of the measurements is determined by the reading devices. A conventional geological compass has graduation lines every 2° for the horizontal circle and every 5° for the dip angle. The standard deviation of the raw readings can be estimated as about one third of the respective graduation interval. Due to the limited accuracy of representing a geological feature by locally attaching a rather small test plate the attainable precision of the dip angle (θ) and the dip azimuth (α) is typically no better than 2°. Further sources of possibly much larger errors are inadequate levelling due to difficult geological compass handling, visual observation of the Bull's eye level, visual reading of the graduation, and the subsequent manual recording of the compass data.

SUMMARY OF THE INVENTION Therefore, there may be a need to provide a device for and a method of determining an orientation of a plane in space — i.e., the dip angle and the dip azimuth of the plane — which may be easier to handle and less prone to errors.

This need may be met by a device for and a method of determining an orientation of a plane in space, by a geological compass for determining an orientation of a plane in space, by a computer-readable medium and by a program element according to the features of the independent claims. Further embodiments are described in the dependent claims.

According to an exemplary embodiment a device for determining the orientation of a plane in space is provided, the device comprising a first unit adapted to receive a first data set indicative of a first physical parameter, and a second unit adapted to receive a second data set indicative of a second physical parameter. Further the device comprises a calculation unit adapted to calculate a transformation array for a transformation based on the first data set, a transformation unit adapted to transform the second data set by using the transformation array, and a determination unit adapted to determine a first angle indicative of an angular orientation of the object in space based on the transformed second data set. In particular, the first unit and the second unit may be formed or housed by a single unit or by two different units.

According to an exemplary embodiment a geological compass comprises a device according to an exemplary embodiment, comprising a first sensor, and a second sensor, wherein the first sensor is adapted to measure the first data set and wherein the second sensor is adapted to measure the second data set. In particular, the first sensor and the second sensor may be formed or housed by a single sensor or by two different sensors with known relative orientation.

According to an exemplary embodiment a method of determining an orientation of a plane in space comprises receiving a first data set indicative of a first physical parameter, receiving a second data set indicative of a second physical parameter, calculating a transformation array for a transformation based on the first data set. Further, the method comprises transforming the second data set by using the transformation array, and determining a first angle indicative of an angular orientation of the object in space based on the transformed second data set.

According to an exemplary embodiment a program element is provided, which, when being executed by a processor, is adapted to control or carry out a method of determining an orientation of a plane in space, wherein the method comprises receiving a first data set indicative to a first physical parameter, receiving a second data set indicative of a second physical parameter, and calculating a transformation array for a transformation based on the first data set. Further, the method comprises transforming the second data set by using the transformation array, and determining a first angle indicative of an angular orientation in space based on the transformed second data set. According to an exemplary embodiment a computer-readable medium is provided, in which a computer program is stored, which, when being executed by a processor, is adapted to control or carry out a method of determining an orientation of a plane in space, wherein the method comprises receiving a first data set indicative of a first physical parameter, receiving a second data set indicative of a second physical parameter, and calculating a transformation array for a transformation based on the first data set. Further, the method comprises transforming the second data set by using the transformation array, and determining a first angle indicative of an angular orientation in space based on the transformed second data set.

A gist of an exemplary embodiment may be seen in the fact that a determination or evaluation device is provided which can be used in connection with a geological compass. A geological compass using such an evaluation device or unit may be called digital geological compass since the evaluation is done electronically, e.g., by using a computer program implemented as software in the evaluation unit or by using a hard wired circuit or a specialized integrated circuit. Furthermore such a digital geological compass may not require physical levelling; rather the levelling may be performed mathematically as part of the evaluation algorithm. Such a digital geological compass may thus be called a mathematically self-levelling geological compass (GC-MSL). A GC-MSL may overcome some of the problems associated with a conventional geological compass (GC). In contrast to known GC, a GC-MSL may not need a swivelling test plate to represent the surface of the feature whose orientation in space is to be determined. Thus, any surface of the GC-MSL housing may be used as the test plate. Measurements may be taken electronically and may internally be recorded in the device, i.e., the determination device or the GC-MSL. Principal innovative features may be that the compulsory levelling of the geological compass becomes obsolete, that there may be no restrictions on the three- dimensional orientation of the GC-MSL while taking readings e.g., the GC-MSL may even be used vertically or upside-down, and that all data may be readily available in digital form.

In the context of this application, the term "transformation array" may be referring to a one-, two- or three-dimensional array or matrix. In particular, the transformation array may be a transformation matrix which may be used to perform a coordinate transformation, i.e., a transformation which transforms values of physical parameters which are measured in a first coordinate system into a second coordinate system. For example, the first coordinate system may be a coordinate system intrinsic or body fixed to an object or a measuring unit, e.g., a geological compass, while the second coordinate system may be a coordinate system external to the object or measuring unit, e.g., a coordinate system relating to the gravity field and/or the magnetic field of the earth.

Next, further exemplary embodiments of the device for determining the orientation of a plane in space will be explained. However, these embodiments also apply to the geological compass for determining the orientation of a plane in space, to the computer-readable medium and to the program element.

According to another exemplary embodiment of the device the first physical parameter represents a deviation from the fall line. According to another exemplary embodiment of the device the first data set is measured by an inclination sensor. In particular, the first data set may be representative of two linearly independent inclination directions. For example the inclination sensor may comprise two independent inclination sub-sensors. One of these two independent sub-sensors may be adapted to measure an inclination in a first direction, e.g., an x-direction of a body fixed coordinate system, while the other one of the sub-sensors may be adapted to measure the inclination in a second direction, e.g., a y-direction of the body fixed coordinate system. However, the two directions do not have to be perpendicular to each other, but preferable they are linearly independent of each other, so that from the measured two inclinations the independent inclination components in a Cartesian coordinate system can be easily derived by known calculations.

According to an exemplary embodiment of the device the first data set is measured by an acceleration sensor. In particular, the first data set may representative of three linearly independent acceleration directions. For example the acceleration sensor may comprise three independent acceleration sub-sensors. One of these three independent sub-sensors may be adapted to measure an acceleration in a first direction, e.g., an x-direction of a body fixed coordinate system, the second one of the sub-sensors may be adapted to measure the acceleration in a second direction, e.g., a y-direction of the body fixed coordinate system, while the third one of the sub- sensors may be adapted to measure the acceleration in a third direction, e.g., a z- direction of the body fixed coordinate system. However, the three directions do not have to be perpendicular to each other, but preferable they are linearly independent of each other, so that from the measured three accelerations the acceleration components in a Cartesian coordinate system can be easily derived by known calculations. The acceleration sensor may be implemented by using known force detectors.

According to another exemplary embodiment of the device the second data set is measured by a magnetic field sensor. In particular, the second data set may be indicative of three linearly independent components of the magnetic field. The magnetic field sensor may be formed by one or more known magnetometers. For example the magnetic field sensor may comprise three independent magnetic field sub-sensors. One of these three independent sub-sensors may be adapted to measure a magnetic field in a first direction, e.g., an x-direction of a body fixed coordinate system, the second one of the sub-sensors may be adapted to measure the magnetic field in a second direction, e.g., a y-direction of the body fixed coordinate system, while the third one of the sub-sensors may be adapted to measure the magnetic field in a third direction, e.g., a z-direction of the body fixed coordinate system. However, the three directions do not have to be perpendicular to each other, but preferable they are linearly independent of each other, so that from the measured three magnetic field components the magnetic field components in a Cartesian coordinate system can be easily derived by known calculations. That is, the first angle may be associated with the point of the compass, while the second angle may be associated with the zenith angle, i.e. the angular deviation from the horizon.

According to another exemplary embodiment the determination unit is further adapted to determine a second angle of the object in space, wherein the second angle is linearly independent of the first angle. In particular, the first angle may be the so- called dip azimuth counted from magnetic North, while the second angle may be the dip angle counted from the horizon.

Next, further exemplary embodiments of the geological compass will be explained. However, these embodiments also apply to the device and to the method for determining the orientation of a plane in space, to the computer-readable medium and to the program element.

According to another exemplary embodiment of the geological compass the first sensor is an acceleration sensor. In particular, the acceleration sensor is adapted to measure three linearly independent components of the acceleration. Alternatively or additionally the first sensor may be a senor adapted to measure an inclination. In particular, the inclination sensor is adapted to measure two linearly independent inclinations.

By using an acceleration sensor and/or an inclination sensor an effective way for measuring the angular orientation of the geological compass with respect to the fall line or to the gravity field of the earth may be provided. Thus, it may be possible to use the corresponding information, i.e., the measured angular orientation, in order to omit the physical levelling of the geological compass as necessary in the case of known geological compasses. Thus, the handling of the geological compass according to an exemplary embodiment may become easier than the handling of known geological compasses. In particular, the data of the acceleration sensor and/or the inclination sensor may be used to perform a coordinate transformation of the second data set, e.g., a data set representative of the azimuth of the geological compass, which may be measured by a magnetic field sensor.

According to another exemplary embodiment the geological compass further comprises a temperature sensor, wherein the temperature sensor is adapted to measure a temperature, and wherein the determination unit is adapted to determine the first angle and/or the second angle under consideration of the measured temperature. By the provision of a temperature sensor, e.g., a digital thermometer, it may be possible to use the measured temperature in order to improve the accuracy of the angle determination, since the measurement of the first sensor and/or the second sensor may be temperature dependent.

According to another exemplary embodiment of the geological compass the first sensor and/or the second sensor is adapted to measure the first data set and/or the second data set for a predetermined time period. In particular, the determination unit may be adapted to determine the first and/or the second angle based on the first data set and/or the second data set averaged over the predetermined time period or otherwise transformed from the predetermined time period to a single epoch.

For example, the first data set and the second data set is sampled for a time period between 0.1 second and 10 seconds in particular between 0.5 seconds and 5 seconds, preferably for 1 second by a rate between 1 Hz and 10 kHz, in particular at a rate between 10 Hz and 1 kHz, preferably at a rate of 100 Hz. When using such a rate the averaging may be done over 50 measured samples, i.e. single measurements. By using such an averaging or transformation of the data sets measured or sampled by the first and second sensors it may be possible to increase the accuracy of the determined orientation. In particular, the precision of the determined orientation may be increased; sensor faults and data outliers may be detected and mitigated, and handling errors (e.g., inappropriate moving of the geological compass during the measurement period) may be detected and signalled.

According to another exemplary embodiment the geological compass further comprises a wireless data communication interface which can be used to transfer data to and/or from the geological compass to another device, e.g., a personal computer, a PDA or another electronic device. Such a wireless data communication may be based on the so-called Bluetooth technique.

According to another exemplary embodiment the geological compass further comprises an analyzing unit adapted to calculate standard errors and/or confidence intervals relating to the first angle and/or second angle, and wherein the analyzing unit is preferably further adapted to create pole diagrams.

By providing such an analyzing unit it may be possible to increase the flexibility and the possible field of application of the device, e.g., parts of the analysis of the determined orientations may already be implemented into the geological compass, thereby reducing the need for subsequent post-processing of the collected data and providing a means for assessing the data quality and the results already during the field work.

Next, further exemplary embodiments of the method of determining the orientation of a plane in space will be explained. However, these embodiments also apply to the device for determining an angular orientation of an object in space, to the geological compass, to the computer-readable medium and to the program element.

According to another exemplary embodiment the method further comprises determining a second angle indicative of an angular orientation in space, wherein the second angle is linearly independent of the first angle.

According to another exemplary embodiment of the method the first angle is determined based on the equation:

—m^b sin ω + m^h cos ω tanα = m^b cos θ cos ω + m^b _v cos θ sin ω + m_: ^b sin θ with wherein a is the first angle, namely the dip azimuth of the plane counted from magnetic north, ω is an angle indicating the deviation of the x -axis from the fall line, θ represents the deviation of the plane from the horizon, m^b represents the i^th component of the second physical parameter expressed in the body-fixed coordinate system, and αf represents the i^th component of the first physical parameter expressed in the body-fixed coordinate system whose x^b and y^b axes are parallel to the plane i.e., whose x^b anay^b axes represent the test plate abutted on the plane whose orientation is to be determined. In both equations, the signs of the numerator and of the denominator correspond respectively to the signs of sinα, cosα , sinω, and costy, and determine the quadrants of the two angles unambiguously.

According to another exemplary embodiment of the method the second angle is determined based on the equation: wherein θ represents the second angle of the plane, and wherein a_t ^h represents the i^th component of the first physical parameter expressed in the body-fixed coordinate system whose x^b andy^b axes are parallel to the plane i.e., whose x^b and y^b axes represent the test plate abutted on the plane whose orientation is to be determined. The signs of the numerator and of the denominator are equal to the signs of sin θ and cos θ , respectively, and determine the quadrant of θ unambiguously.

The theoretical background of the above mentioned equations will be described in detail in connection with the Fig. 1 and Fig. 2.

According to another exemplary embodiment the method further comprises converting the first angle from an angle relating to magnetic North to an angle relating to any chosen earth fixed reference direction, e.g., to geographical North. This can be accomplished using a third data set consisting of a first data sub-set related to the magnetic field on earth, e.g., a known numerical model of the earth magnetic field, and a second data sub-set related to the position on earth, e.g., obtained from a positioning device like a GPS receiver or from user input based on a map.

According to an exemplary aspect of the present invention a digital, mathematically self-levelling geological compass (GC-MSL) may be provided which may not require the physical levelling of the compass any longer. Instead of a swivelling test plate, as used in known geological compasses, the GC-MSL according to this aspect itself is attached to the geological surface in any suitable orientation. A sensor combination which may be used for the GC-MSL comprises a three-dimensional accelerometer and a three-dimensional magnetic field sensor wherein the device, e.g., the GC-MSL, is adapted to compute the dip angle and dip azimuth of the geological surface i.e., the dip angle and the azimuth of the fall line representative of the part of the geological surface to which the GC-MSL is attached. Experimental results show that the dip angle and azimuth of the fall line can be obtained with a precision better than 1° using a few seconds of data from these two sensor triads.

Advantages of the GC-MSL according to this exemplary aspect in comparison to a conventional geological compass may be: (a) levelling of the geological compass may not be required any longer; (b) attaching the test plate of the geological compass to the geological feature may be possible in any suitable orientation; (c) the test plate may not have to be swivelling, and thus e.g. one face of the housing of the geological compass can be the test plate; (d) it may allow for true one-hand operation; (e) it may allow measurements at geological features which are inaccessible or difficult to measure when using a conventional compass that needs to be visible and levelled while the readings are taken; (f) it may save time in the measurement process; (g) it may output digital data; (h) it may provide high precision and reliability.

The digital geological compass may be further developed by (i) using wireless communication with a (pocket) PC in the field, (ii) optionally converting azimuths from magnetic North to a different reference direction e.g., geographical North, (iii) providing the orientation of linear elements as represented e.g., by an edge of the GC-MSL housing, in addition to the orientation of the fall line of surfaces, (iv) analyzing the data on-line in the field to provide statistical information, e.g., standard errors, confidence intervals, to safeguard against undetected sensor faults and improper handling e.g., by statistical outlier detection or time series analyses, and to automatically create graphical representations of the collected data, e.g., pole diagrams. According to this aspect the dip angle is referenced to the local vertical using accelerometer measurements of the local gravity vector. The dip azimuth is derived from magnetometer measurements of the local magnetic field vector. In particular, the adaptation of such a sensor assembly for geological measurements and the derivation of the required data processing algorithms may represent a new and inventive novel approach. By using such a geological compass a digital, mathematically self-levelling geological compass may be provided that does not require physical levelling any longer; that may be manufactured small and lightweight, and that may yield accurate dip angle and dip azimuth measures within less than a few seconds.

The aspects defined above and further aspects of the invention are apparent from the examples of embodiment to be described hereinafter and are explained with reference to these examples of embodiment.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described in more detail hereinafter with reference to examples of embodiment but to which the invention is not limited.

Fig. 1 illustrates a body-fixed coordinate system in which sensor readings can be performed, and a coordinate system in which the orientation of a plane can be expressed.

Fig. 2 illustrates rotations of the body-fixed coordinate system of Fig. 1.

Fig. 3 schematically illustrates an experimental setup for testing an exemplary embodiment of a geological compass.

Fig. 4 schematically illustrates an enlarged view of the geological compass of Fig. 3. Fig. 5 schematically shows testing results obtained using the experimental setup shown in Fig. 5.

Fig. 6 shows a known geological compass and a schematic display of the orientation of a geological feature.

DESCRIPTION OF AN EXEMPLARY EMBODIMENT

The illustration in the drawings is schematical. In different drawings, similar or identical elements are provided with the same reference signs.

In the following, referring to Figs. 1 and 2, the theoretical background of an exemplary embodiment of a geological compass will be described in more detail.

An assembly of three accelerometers and three magnetometers can be used to determine the local gravity vector and the local earth magnetic field vector in a body- fixed coordinate system (x y z ). It can be assumed that this coordinate system is orthogonal, with its x^by^b-p\ane representing the fixed test plate of a digital, mathematically self-levelling geological compass (e.g., one face of the housing). For simplified data processing and for optimum accuracy over all possible dip angles and dip azimuths, the individual sensors are preferably aligned with the axes of the body- fixed coordinate system, thus forming substantially orthogonal and mutually aligned accelerometer and magnetometer triads.

The digital, mathematically self-levelling geological compass (GC-MSL) 100 can — without levelling — be held against a geological surface 101 and may yield accurate measures of the azimuth α 102 and the dip angle θ 103, wherein the dip angle θ 103 corresponds to the inclination angle and can be measured between the geological surface 101 and a horizontal plane schematically depicted by the line 104 in Fig. 1. In fact, α and θ can be computed from the sensor output by exploiting the relation between the body-fixed coordinate system, shown as 105 in Fig. 1, and the local-level coordinate system, formed by the magnetic North 106, the magnetic East 107 and the vertical 108. Within this embodiment it is assumed that the local-level coordinate system is defined by the local vertical, i.e., the direction "up", the opposite to the gravity vector, and by the local magnetic North direction, see Fig. 1.

For mathematical derivations it is assumed that the GC-MSL is being attached to the geological feature with the x^by^b plane parallel to the feature (see Fig. 1). So, the fall line of the geological feature is contained in the x^by^b plane, but not generally aligned with either axis. In order to achieve this alignment, the body- fixed coordinate system is rotated about its z*-axis by an angle ω such that the resulting x-axis (x¹) points along the fall line (see Fig. 2a), i.e., the angle ω corresponds to the angle between the fall line and the x direction of the coordinate system 105: cos ω sin ω 0 y - sin ω cos ω 0 y (1)

0 0 1

The angle between the x'-axis and the local horizon is exactly the required dip angle θ , and the y^l -axis is horizontal. So, we obtain a coordinate system whose z- axis points upward (along the local vertical) and whose x-axis is horizontal and points along the azimuth a when rotating the (xV z¹) coordinate system by - θ about the y¹ -axis, see Fig. 2b: cos θ 0 sin θ y 0 1 0 y (2) - sin θ 0 cos θ

Combining both rotations (1) and (2) gives x cos θ cos ω cos θ sin ω sin θ y = R(θ,ω) y — sin ω cos ω 0 y (3)

- sin#cos&> - sinøsinω cos#

Considering original acceleration measurements (a^ ,a_y ^h ,a_: ^h) of a static GC-

MSL, wherein the different components relate to the measured accelerations along the axes of the body-fixed coordinate system, it can be realised that their transformation into the {x²y²^) system yields the components of the local gravity vector g which is parallel to the z² axis: (4)

Thus, eq. 4 with the transformation matrix R{θ,ώ) of eq. 3 represents an equation system from which the unknown angles ω and θ can be computed. The knowledge of g (i.e., magnitude of the local gravity) is not required, since the first two components of the vector equation (4) are sufficient to calculate the angles ω and θ . Mathematically, there are two solutions to eq. 4, one with x^λ pointing downward and one with x¹ pointing upward along the fall line. By including the constraint that the dip shall always point downwards (i.e., sin ^ > 0 ), this ambiguity can be solved and a unique solution is obtained as follows: a_x ^b cos ω + a* sin ω _ yj (α* f + (a_y" f tan <9 = (6)

-a, -a\ where the signs of the numerators and of the denominators are equal to the signs of sin ω , cos ω , sin θ and cos θ , respectively, and thus indicate the quadrants of θ and ω unambiguously.

It is pointed out that ω is undefined if the dip angle is 0 — there is no fall line in this case — , but that eq. 5 yields the correct value of θ even in this case. It is further pointed out that eq. 6 can be derived from eq. 3 by using the second component of the vector equation 3, while eq. 5 can be derived by using the first component of eq. 3.

Eq. 6 shows that all three original acceleration measurements are required to compute the dip angle. It is not possible to determine θ using only two accelerometers unless the magnitude of g is known and either a,^b is one of the measured accelerations, or a restriction on the three-dimensional orientation of the digital geological compass is applied, e.g., that it is not used with its z*-axis pointing below the horizon. Thus, according to an exemplary embodiment it is possible to only provide two accelerometers but further impose restrictions on the orientation of the digital geological compass and provide the magnitude of the gravity field at the respective position of the digital geological compass.

In the following the computation of the dip azimuth is described. The projection of the earth magnetic field vector onto the horizontal (x²y )-plane defines magnetic north in that plane, see Fig. 2c. The angle a counted clockwise from that projection to the x²-axis is the dip azimuth that would also be measured with a levelled conventional geological compass. However, the projection can be computed from the original magnetometer measurements (m_x ^b , m_y ^b ,m_: ^b) taken in the body- fixed frame by transforming them into the (x²y²z²) system using eq. 3 — thus replacing physical levelling of the digital geological compass by mathematical levelling:

a can then be computed from Substituting eq. 7 into eq. 8 finally yields: m_x cos θ cos ω + m_y cos θ sin ω + m. sin θ where the signs of the numerator and the denominator are equal to the signs of cosα and sin a , respectively, and thus indicate the quadrant of a unambiguously.

The so-called strike azimuth i.e., the azimuth of the intersection between the measured plane and the horizon, when preferred over the dip azimuth, can be obtained by subtracting 90° from a . In fact, the azimuth a of the fall line has been derived above as rotated by 90° with respect to that intersection. Thus, eq. 9 yields a value that correctly represents the orientation of the plane even if the plane is vertical i.e., even if the azimuth of the fall line is undefined. The strike azimuth will not be considered further in this application. If the geological feature to be measured is horizontal, then of course its azimuth a (like ω ) is undefined. This is a fundamental geometric property rather than a weakness of the GC-MSL, and affects all compasses.

Eq. 9 clearly shows that all three components of the magnetic field vector must be measured in the body-fixed coordinate system in order to determine the dip azimuth. It may be possible to determine the dip azimuth using less than three measured components of the magnetic field if the local magnitude and direction of the field are known and restrictions on the orientation of the body-fixed frame apply.

Numerically, eq. 6 yields values of θ between 0 and 180°. hi order to account for the usual definition of dip angles, preferably the computed dip angle θ' and azimuth a' are introduced such that always 0 < θ' < 90° :

In the above described theoretical background it is assumed that the three acceleration sensors and the three magnetometers are perfectly orthogonal and perfectly aligned with the body-fixed coordinate system, the x y -plane of which was chosen to define the test plate in the exemplary embodiment of a GC-MSL. Such a sensor assembly can hardly be manufactured. Furthermore, it is assumed above that the individual sensor output equals exactly the projection of the corresponding vector (gravity or magnetic field) onto the sensor axis. In reality, the output of such sensors may be affected by biases (non-zero output with zero input), scale factor errors, random noise and higher order errors.

However, most of these errors (alignment errors and sensor errors) may be calibrated beforehand and may be easily corrected for in real-time, such that the corrected measurements represent the values a_x ^b, ..., m_: ^b used above. For example, Stork T (2000) "Electronic Compass Design using KMZ 51 and KMZ 52",

Application Note, Philips Semiconductors, Systems Lab, Hamburg, 38p, which is herby incorporated herein by reference, provides useful information about the calibration of the sensor misalignment, and gives the "rule-of-thumb" that the degree of non-orthogonality will create a similar degree of error in the measured azimuth of an electronic compass. Furthermore, it is known from experimental analysis of error influences on the calibration of the magnetic compass that calibration may improve the azimuth results significantly from, e.g., 8° error without calibration to about 0.3° error when using the calibration results. These findings may be applicable to the digital geological compass.

Furthermore, the errors may additionally vary slowly over time and depend on sensor temperature. While the former effect must be included in the error budget of the digital geological compass or mitigated by selecting sensors that exhibit low drift, the latter effect can be modelled and corrected for in case also a digital temperature sensor is included in the digital geological compass.

According to an exemplary embodiment of a geological compass inevitable random noise can be mitigated by averaging raw sensor output, e.g., measured data sets of the acceleration sensors and/or magnetic field sensors, over a suitable time interval. This may also allow for quality control of the raw data, e.g., to detect whether the sensor is sufficiently static during the measurement period. A generally valid optimum averaging time cannot be given; a suitable time needs to be found depending on the noise characteristics of the sensors contained in the digital geological compass. An indication is given later on in this application.

In the following an exemplary embodiment of a digital geological compass, namely of a GC-MSL, will be described in more detail. Furthermore, experimental results will be described. The GC-MSL comprises three solid state accelerometers, three thin film magnetometers and one temperature sensor. All sensors fit into a small and lightweight housing.

After calibration of the sensor unit which can be performed by using software and a dedicated measurement procedure, the accelerometer and magnetometer outputs refer to axes aligned with the body-fixed coordinate system within about 0.3°. 100 Hz raw sensor data are output by the sensor unit via its serial interface and can be recorded on a laptop computer. These raw sensor data can be post-processed using a known program, e.g. MATLAB, wherein the post-processing typically consists of (i) conversion from raw data to calibrated sensor output (a_x ^b, ..., m_: ^b), (ii) reducing the data rate by averaging a number of consecutive epochs, e.g. 50 epochs which yields 2Hz data, and (iii) computation of dip angle and azimuth using eqs. 5, 6, 9, and 10.

Recording and post-processing of the raw data allows for extensive data analysis during an experiment. However, all the required algorithms can be implemented in a digital geological compass for real-time operation, and a separate post-processing is not necessary.

In order to allow for extensive testing of a digital geological compass, a non- magnetic and non-ferrous test jig can be used. Fig. 3 schematically shows such a jig 301. The sensor unit 302 can be rigidly attached to a first plate 303 of the jig which can be pivoted about a horizontal axis 304 which can in turn be rotated about a vertical axis 305. Furthermore, the jig provides bolts or graduations to determine the rotation angle of the first plate 303 about the two axes 304 and 305. Such a jig allows establishing well known and reproducible orientations in space and removes the uncertainty associated with abutting the digital geological compass onto a real geological feature which is identical for the conventional geological compass and for a digital geological compass and will thus not be investigated in this application.

In the following a field test and the resulting deviations of computed dip angles and dip azimuths are described. The field test demonstrates the overall performance as obtained using a low-cost sensor assembly once it has been properly calibrated.

The field test was carried out in a quarry which is situated in non-magnetic bedrock. In order to provide a stable reference, the jig 301 was mounted on a plaster bed 306 and was carefully levelled using a precision spirit level. A Suunto KB-14 sighting compass was used to determine the magnetic azimuth of the jig. The sensor unit 302 housing the sensors, i.e. the acceleration sensors, the magnetic field sensors and the temperature sensor, was rigidly attached to the plate 303. The orientation of this plate in terms of the angles θ and a was then changed to about 140 different states involving a range of 0° < a < 360° for the dip azimuth and 15° < θ < 90° for the dip angle. At each of these states the the sensor unit 302 was static for 10-20 seconds, and raw sensor output was recorded at 100Hz. The dip angle and azimuth were then computed separately from each consecutive batch of 50 epochs, corresponding to a period of 0.5 seconds of raw data.

Fig. 4 schematically shows an enlarged view of the jig 301 which comprises a sensor unit 302 housing the sensors, i.e. the acceleration sensors, the magnetic field sensors and the temperature sensor. The sensor unit 302 is fixed to a first plate 303 which can be pivoted about a horizontal axis. The first plate 303 is pivotably fixed between two plates 407 and 408 which are perpendicular to the horizontal axis. The two plates 407 and 408 are fixed to a second plate 409, which can be rotated about a vertical axis. Thus, the sensor unit 302 can be rotated about two perpendicular axes corresponding to the two degrees of rotation of a geological surface.

Fig. 5 shows the deviations δθ = θ' - θ''^e (upper portion of Fig. 5) and δa = a' - a^μe (lower portion of Fig. 5) of the computed dip angle and azimuth from the respective setting (and graduation/bolt reading) of the jig. The plot represents more than 5000 pairs of computed values of θ and a covering the full azimuth range of 360° and an inclination range of 75°.

The non-zero mean value of 1.3° for δa can be attributed to a bias of the jig orientation as established using the conventional Suunto compass.

The standard deviation (std) of δθ and δa is 0.1° and 0.5°, respectively. All dip angle deviations and most of the azimuth deviations are within ±1° about the respective mean value (shaded area in Fig. 5). This indicates remarkably high precision, given the short measurement time of only 0.5 seconds per sample, and the contribution of the jig (slackness, and standard deviation of graduation reading were estimated with about 0.1-0.2°). Summarizing, according to one aspect a GC-MSL is provided that is suitable to achieve a precision of 1 ° for both azimuth and dip angle with various three- dimensional orientations of the sensor unit. Further improvements may include the selection of optimum sensor elements, the realization of wireless data transmission between the sensor unit and/or digital geological compass and a determination device, e.g. a PC or PDA, the optimization of the calibration procedure, and an error analysis including random and systematic effects.

It should be noted that the term "comprising" does not exclude other elements or features and the "a" or "an" does not exclude a plurality. Also elements or features described in association with one embodiment or aspect may be combined with elements or features described in association with another embodiment or aspect. It should also be noted that reference signs in the claims shall not be construed as limiting the scope of the claims.

Claims

Claims:

1. A device for determining an angular orientation of a plane in space, the device comprising: a first unit adapted to receive a first data set indicative of a first physical parameter, a second unit adapted to receive a second data set indicative of a second physical parameter, a calculation unit adapted to calculate a transformation array for a transformation based on the first data set, a transformation unit adapted to transform the second data set by using the transformation array, and a determination unit adapted to determine a first angle indicative of an angular orientation of a plane in space based on the transformed second data set.

2. The device according claim 1, wherein the first physical parameter represents a deviation from the fall line.

3. The device according claim 2 wherein the first data set is measured by an inclination sensor.

4. The device according claim 3, wherein the first data set is representative of two linearly independent inclination directions.

5. The device according claim 2, wherein the first data set is measured by an acceleration sensor.

6. The device according claim 5, wherein the first data set is representative of three linearly independent acceleration directions.

7. The device according to any one of the claims 1 to 6, wherein the second data set is measured by a magnetic field sensor.

8. The device according to claim 7, wherein the second data set is indicative of three linearly independent components of the magnetic field.

9. The device according to any one of the claims 1 to 8, wherein the determination unit is further adapted to determine a second angle in space, wherein the second angle is linearly independent from the first angle

10. A geological compass comprising: a device according to anyone of the claims 1 to 9, a first sensor, a second sensor, wherein the first sensor is adapted to measure the first data set, wherein the second sensor is adapted to measure the second data set.

11. The geological compass according to claim 10, wherein the first sensor is an acceleration sensor.

12. The geological compass according claim 11, wherein the acceleration sensor is adapted to measure three linearly independent components of the acceleration.

13. The geological compass according to claim 10, wherein the first sensor is a sensor adapted to measure an inclination.

14. The geological compass according to claim 13, wherein the inclination sensor is adapted to measure two linearly independent inclinations.

15. The geological compass according to any one of the claims 10 to 14, further comprising: a temperature sensor, wherein the temperature sensor is adapted to measure a temperature, and wherein the determination unit is adapted to determine the first angle and/or the second angle under consideration of the measured temperature.

16. The geological compass according to any one of the claims 10 to 15, wherein the first sensor and/or the second sensor is adapted to measure the first data set and/or the second data set for a predetermined time period.

17. The geological compass according to claim 16, wherein the determination unit is adapted to determine the first and/or the second angle based on the first data set and/or the second data set averaged over the predetermined time period.

18. The geological compass according to any one of the claims 10 to 17, further comprising: a wireless data communication interface.

19. The geological compass according to any one of the claims 10 to 18, further comprising: an analyzing unit adapted to calculate standard errors and/or confidence intervals relating to the first angle and or second angle, and wherein the analyzing unit is preferably further adapted to create pole diagrams.

20. A method of determining an orientation in space, the method comprising: receiving a first data set indicative to a first physical parameter, receiving a second data set indicative of a second physical parameter, calculating a transformation matrix for a coordinate transformation based on the first data set, transforming the second data set by using the transformation matrix, and determining a first angle indicative of an angular orientation in space based on the transformed second data set.

21. The method according claim 20, further comprising: determining a second angle indicative of an angular orientation in space, wherein the second angle is linearly independent of the first angle.

22. The method according to claim 20 or 21, wherein the first angle is determined based on the equation:

— /w* sin ω + m^b cos ω tanα = - ^y m_x cos θ cos ω + m_y cos θ sin ω + m_z sin θ wherein α is the first angle; ω represents an angular deviation from the fall line, θ represents an angular deviation of the plane from the horizon, and /w₍* represents the i^th component of the second physical parameter.

23. The method according to claim 21 or claim 22, wherein the second angle is determined based on the equation: wherein θ represents the second angle of the object, and wherein α_;* represents the i^th component of the first physical parameter.

24. The method according to any one of the claims 20 to 23, further comprising: converting the first angle from an angle relating to magnetic North to an angle relating to geographical North.

25. The method according to claim 20, wherein the first data set comprises a first data subset and a second data subset, wherein the first data subset relates to a position on earth, and wherein the second data subset relates to the earth magnetic field at the position on earth.

26. A program element, which, when being executed by a processor, is adapted to control or carry out a method of determining an orientation of a plane in space, the method comprising: receiving a first data set indicative to a first physical parameter, receiving a second data set indicative of a second physical parameter, calculating a transformation array for a transformation based on the first data set, transforming the second data set by using the transformation array, and determining a first angle indicative of an angular orientation in space based on the transformed second data set.

27. A computer-readable medium, in which a computer program is stored which, when being executed by a processor, is adapted to control or carry out a method of determining an orientation of an object in space, the method comprising: receiving a first data set indicative to a first physical parameter, receiving a second data set indicative of a second physical parameter, calculating a transformation array for a transformation based on the first data set, transforming the second data set by using the transformation array, and determining a first angle indicative of an angular orientation in space based on the transformed second data set.