WO2006018791A1 - Method and apparatus for calibrating the rotational relationship between two motion sensors of a sensor system - Google Patents
Method and apparatus for calibrating the rotational relationship between two motion sensors of a sensor system Download PDFInfo
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- WO2006018791A1 WO2006018791A1 PCT/IB2005/052643 IB2005052643W WO2006018791A1 WO 2006018791 A1 WO2006018791 A1 WO 2006018791A1 IB 2005052643 W IB2005052643 W IB 2005052643W WO 2006018791 A1 WO2006018791 A1 WO 2006018791A1
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
- G01P21/00—Testing or calibrating of apparatus or devices covered by the preceding groups
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
- G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices
Definitions
- the present invention relates to a method and apparatus for calibrating sensor systems and, particularly to a method and apparatus for calibrating motion sensor systems.
- Sensors are devices or means capable of sensing ( or responsive to ) specified measurement values and converting them into usable output signals according to certain rules. Sensors ordinarily comprise sensitive element which directly responds to the measurement values, converting element which generates output signals, and corresponding electronic circuits.
- Motion sensors as sensors having their own coordinate systems, are capable of converting the motion signals of an object into detectable electrical signals, such as the acceleration sensor and gyrocompass sensor.
- the acceleration sensor and gyrocompass sensor are ordinary measurement instruments for shock and vibration measurements and motion tracking in many fields such as industry and national defense, which are especially applicable in vibration measurement and motion tracking in the fields of seismology, architecture, military, transportation, machinery, navigation and the like.
- the acceleration sensor is a measurement instrument for converting the physical signal of acceleration into an electrical signal which is easy to be measured.
- the output value of the measurement of the acceleration sensor is a voltage value reflecting the acceleration.
- the acceleration sensor in the form of an IC chip manufactured by the Hitachi Metals Ltd, Tokyo, Japan is a three-dimentional piezoresistance acceleration sensor capable of detecting the accelerations in the three axial directions ( X, Y and Z ).
- This sensor is a very small and thin three-dimensional acceleration sensor of the semiconductor type which is highly sensitive, shock-proof and pressing proof. More information relating to this acceleration sensor can be obtained from the web site http://www.hitachimetals. co.jp/e/p rod/prod 06/p06 10.htm. Those informations are incorporated herein by reference.
- the gyrocompass sensor is a measurement equipment for converting the physical signal of angular velocity into electrical signal which is an easy to be measured.
- the output value of measurement of the gyrocompass sensor is an electrical signal reflecting the angular velocity.
- two or more motion sensors are ordinarly needed in a sensor system, for example, two three-dimensional motion sensors are needed in systems, such as the three-dimensional hand-writing recognition system, inertial measurement unit, robotic arm motion measurement system, aerial guidance system, appliance remote controller and the like, to sense the motion of the sensor system in the three-dimensional space.
- the two or more motion sensors in a sensor system are motion sensors of the same type, for example, both of them are acceleration sensors or gyrocompass sensors, then it is necessary to calibrate the positional relationship between the coordinate systems of those two or more motion sensors, such that the output values of those two or more motion sensors in the system are transformed into the same coordinate system, so as the motion locus of the sensor system can be tracked by measuring the output values of those motion sensors.
- the positional relationship between two motion sensors in a sensor system comprises a translational relationship and a rotational relationship therebetween.
- the translational relationship between two motion sensors is determined by the design and construction of the system electronic circuitry board, which is relatively easy to determine by measurement or other approaches.
- the rotational relationship between two motion sensors refers to rotating the coordinate system of one of the sensors by a specific angle required by the coordinate system of the other sensor, such that the rotational angle of the coordinate system of one of the sensors can achieve the requirements of design with respect to the coordinate system of the other sensor, for example parallel to each other.
- two or more sensors are parallelly placed during the design of the electronic circuitry board, and the parallelism and freedom from rotation of the coordinate systems of the two or more sensors are realized by an as-strict-as-possible manufacturing process in their production.
- This approach imposes severe requirements upon the manufacturing process.
- the second approach is the measurement approach, in which the angles between the two or more acceleration sensors are measured by angle measurement instrument. The requirement on the measurement accuracy of the angle measurement instrument is very high in order to obtain accurate measurements.
- the rotational relationship between the first motion sensor and the second motion sensor is obtained as follows: obtaining the residual error in a reference coordinate system of the output values of the first motion sensor and the second motion sensor, and obtaining the rotational relationship by processing the residual error according to an optimized strategy.
- It is another object of the present invention to provide a calibration apparatus for calibrating the rotational relationship between a first motion sensor and a second motion sensor in a sensor system the apparatus comprises: a determining means for determining a minimal number of measurements based on the number of dimensions of the coordinat system of said first motion sensor and the number of dimensions of the coordinate system of said second motion sensor; a measuring means for measuring said sensor system for a specific number of measurements to obtain the output values of said first motion sensor and said second motion sensor during each of the measurements, said specific number is not less than said minimal number of measurements; and an acquisition means for obtaining the rotational relationship between said first motion sensor and said second motion sensor based on said measured output values.
- said computer program comprises: code for determining a minimal number of measurements based on the number of dimensions of the coordinate system of said first motion sensor and the number of dimensions of the coordinate system of the second motion sensor; code for performing a specific number of measurements on said sensor system to obtain the output values of said first motion sensor and said second motion sensor during each of the measurements, said specific number is not less than said minimal number of measurements; and code for obtaining the rotational relationship between said first motion sensor and said second motion sensor based on said measured output ralues.
- Fig. 1 is a flow chart showing the method of calibrating the rotational relationship of two motion sensors in a calibration sensor system according to the present invention
- Fig. 2 is a schematic diagram showing an apparatus for calibrating the rotational relationship of two motion sensors in a sensor system according to the present invention.
- Fig. 3 is a schematic diagram showing a motion tracking system according to the present invention.
- Fig. 1 shows a flow chart of the method of calibrating the rotational relationship of two motion sensors in a sensor system according to the present invention.
- the two motion sensors in the sensor system are both acceleration sensors having three dimensional coordinate system. Let one of the two acceleration sensor be the first sensor and the another acceleration sensor the second sensor.
- a specific number of measurements of the output values of the two motion sensors in the sensor system is determined (SI lO).
- SI lO a specific number of measurements of the output values of the two motion sensors in the sensor system.
- both the coordinate system of the first sensor and the coordinate system of the second sensor are three-dimensional coordinate systems, thus the minimal number of measurements is 3. In order to reduce the systematic errors and observational errors, the specific number of measurements is greater than 3.
- the acceleration of the first sensor and the acceleration of the second sensor are measured (S 120).
- the acceleration of the sensor system is rendered unchanged during measurement, that is, the accelerations of the first sensor and the second sensor are measured, respectively, during static or parallelly translation period of the sensor system. It is relatively difficult to keep the sensor system in the parallelly translation state and perform measurement, and by comparision, it is relatively easy to realize the static measurement condition.
- the residual error in one reference coordinate system of the accelerations of the first sensor and the second sensor during this measurement is obtained (S 130).
- the acquirement of the rotational relationship between said coordinate systems can be realized by calculating the residual error in one reference coordinate system between the acceleration of the first sensor and the acceleration of the second sensor.
- the reference coordinate system can be the coordinate system of the first sensor or the coordinate system of the second sensor, or it can be the world coordinate system as well.
- the coordinate system of the first sensor is taken as the reference coordinate system to acquire the residual error between the accelerations of the two sensors.
- ao,, and ai be the accelerations of the first sensor and the second sensor, respectively, in the ith measurement
- the residual error in the coordinate system of the first sensor between the acceleration of the first sensor and the acceleration of the second sensor in the ith measurement is ao , , - Rai,, .
- the number of measurements has reached the specific number (S 140). If the number of measurements is less than the specific number of measurements, the measurements of the accelerations of the first sensor and the second sensor continue. Let the sensor system be in different attitude during each of the measurements. If the measurements are made in the static state of the sensor system, the attitude of the sensor system is changed at the beginning of each new measurement; if the measurements are made in the parallel translation of the sensor system, the attitudes of the sensor system in the measurements are different from one another with respect to the world coordinate system.
- R be the parameter of the rotational relationship between the first sensor and the second sensor, and this parameter can be expressed by a orthogonal matrix of parameters. While R is a 3 x 3 matrix of 9 variables, however, R is a matrix of only three degrees of freedom since R is a orthogonal matrix of parameters.
- any rotation can be expressed by three rotational angles called Euler's angles.
- the rotational relationship between the first sensor and the second sensor can also be expressed by an Euler's angle.
- a rotation can be expressed by the three Euler's angles ( ⁇ , ⁇ , ⁇ ): the first angle of rotation, ⁇ , is the angle of rotation around the Z axis; the second angle of rotation, ⁇ e [0, ⁇ ], is the angle of rotation around the X axis; and the third angle of rotation, ⁇ , is the angle of rotation further around the Z axis.
- this Euler's angle makes it possible to transform the coordinate system of the second sensor to the coordinate system of the first sensor, it can also transform the coordinate system of the first sensor to the coordinate system of the second sensor, and it can further transform the coordinate system of the first sensor and the coordinate system of the second sensor to the world coordinate system.
- the acquisition of the Euler's angle can transform the coordinate system of the first sensor and the coordinate system of the second sensor to the same coordinate system.
- the rotational relationship between the two sensors can also be expressed by the orthogonal matrix of parameters R.
- R is a 2x2 matrix of four variables, however, R is a orthogonal matrix of parameters, thus R is a matrix of only one
- the measurement values of the sensors are the projections of their accelerations on the direction of their coordinate systems, and for the same acceleration, the measurement values of the two sensors are in a certain (fixed) proportion with each other.
- R be the coefficient of proportion between the measurement values of the first sensor and the measurement values of the second sensor, where R is a real number.
- a 0 be the measured acceleration of the first sensor
- Ai be the measured acceleration of the second sensor. They are expressed in the form of matrix as follows:
- A , where ao,i and ai ;1 represent the output values of the two
- the rotational relationship between the two sensors is obtained under the rule of the sum of the squares of the residual errors of the accelerations of the two sensors in the coordinate system of the first sensor being minimum, i.e.
- the minimal number of measurements is determined by the small number of dimensions of the coordinate system in those two coordinate systems. Because the manufacturing cost of the motion detecting system can be greatly increased by the inconsistency of the numbers of dimensions of the coordinate systems of two sensors, there fore, in practical applications, the numbers of dimensions of the coordinate systems of the first and the second sensor are equal in most situations.
- Fig. 2 is a schematic diagram showing an apparatus for calibrating the rotational relationship of two motion sensors in a sensor system according to the present invention.
- the two motion sensors in this embodiment are both three-dimensional acceleration sensor.
- the calibration apparatus 200 comprises: a determining means 210 for determining the minimal number of measurements based on the numbers of dimensions of the coordinate system of said first sensor and the coordinate system of said second sensor; a measuring means 220 for measuring said sensor system for a specific number of measurements to obtain the accelerations of said first motion sensor and said second motion sensor during each measurement, said specific number being not less than said minimal number of measurements; and an acquisition means 230 for obtaining the rotational relationship between said first motion sensor and said second motion sensor based on said measured accelerations.
- the coordinate system of the first sensor and that of the second sensor are both three-dimensional, and the determining that means determines at least three measurements are needed.
- the measuring means 220 is used for measuring said sensor system for the specific number of measurements to obtain the accelerations of said first motion sensor and said second motion sensor during each of the measurements, the accelerations are three-dimensional, and said specific number is not less than said minimal number of measurements (3), i.e., the specific number is equal to or greater than 3.
- the acquisition means 230 acquires directly the rotational relationship between the first motion sensor and the second motion sensor based on the three sets of accelerations of the sensors measured by the measuring means 220.
- the rotational relationship between the first sensor and the second sensor can be expressed by a orthogonal matrix of three degrees of freedom, that is, it can be expressed by the Euler's angles ( ⁇ , ⁇ , ⁇ ). Those Euler's angles can be calculated based on the measured three sets of accelerations of the first sensor and the second sensor, and the rotational relationship between the first motion sensor and the second motion sensor can thus be obtained, while the coordinate system of the first motion sensor and that of the second motion sensor are transformed into the same coordinate system.
- the acquisition means 230 comprises a residual error acquisition means 232 and an optimized processing means 234.
- the residual error acquisition means 232 is used for acquiring the residual errors of the accelerations of the first sensor and that of the second sensor in one reference coordinate system.
- the optimized processing means 234 is used to obtain the rotational relationship by processing said residual errors based on an optimized strategy.
- Said strategy can be: the sum of the squares of the residual errors of the output values of the first motion sensor and the second motion sensor is minimum; the sum of the absolute values of the residual errors of the output values of the first motion sensor and the second motion sensor is minimum; or the weighted sum of the residual errors of the output values of the first motion sensor and the second motion sensor is minimum.
- the present invention can also be implemented by an appropriately programmed computer, with a computer program installed on the computer, that can be a computer program product for calibrating the rotational relationship between a first motion sensor and a second motion sensor in a sensor system
- the computer program comprises: code for determining a minimal number of measurements based on the number of dimensions of the coordinate system of said first motion sensor and the number of dimensions of the coordinate system of said second motion sensor; code for measuring said sensor system for a specific number of measurements to obtain the output values of said first motion sensor and said second motion sensor during each of the measurements, said specific number being not less than said minimal number of measurements; and code for acquiring the rotational relationship between said first motion sensor and said second motion sensor based on said measured output values.
- This computer program product can be stored on a storage carrier.
- FIG. 3 is a schematic diagram showing a motion tracking system according to the present invention.
- the motion tracking system 300 comprises two motion sensors, a first motion sensor 310 and a second motion sensor 311.
- the system further comprises: a calibrating means 200, and a motion tracking means 400 for acquiring the motion locus of the motion tracking system 300 based on the rotational relationship between the coordinate system of said first motion sensor and the coordinate system of said second motion sensor.
- the calibrating means 200 is used to calibrate the rotational relationship between said first motion sensor and said second motion sensor.
- the calibrating means 200 receives the output values of the first motion sensor 310 and the second motion sensor 320, obtains the rotational relationship of those two motion sensors, and then transmits the obtained rotational relationship to the motion tracking means
- the motion tracking means 400 is used to obtain the motion locus of said first motion sensor and said second motion sensor based on the rotational relationship between the coordinate system of said first motion sensor and that of said second motion sensor.
- the motion tracking means 400 receives the output values of the first motion sensor 310 and the second motion sensor 320, and transforms the output values of the first motion sensor and the second motion sensor to the same coordinate system for performing motion tracking based on the rotational relationship between the coordinate system of said first motion sensor and the coordinate system of said second motion sensor.
Abstract
The present invention provides a method and apparatus for calibrating the rotational relationship between a first motion sensor and a second motion sensor in a sensor system, the method comprises the steps of: determining a minimal number of measurements based on the number of dimensions of the coordinate system of said first motion sensor and the number of dimensions of the coordinate system of said second motion sensor; measuring said sensor system for a specific number of measurements to obtain the output values of said first motion sensor and said second motion sensor during each of the measurements, said specific number of measurements is not less than said minimal number of measurements; and obtaining the rotational relationship between the first motion sensor and the second motion sensor based on said measured output values.
Description
METHOD AND APPARATUS FOR CALIBRATING THE ROTATIONAL RELATIONSHIP BETWEEN TWO MOTION SENSORS OF A SENSOR SYSTEM
FIELD OF THE INVENTION
The present invention relates to a method and apparatus for calibrating sensor systems and, particularly to a method and apparatus for calibrating motion sensor systems.
BACKGROUND OF THE INVENTION
The great majority daily lives of people living in the information era are closely related to the development, acquisition, transmission and processing of information resources. As windows of information sensing, acquisition and detecting, sensors of different functions play a very important role in the signal detection and information processing systems. Sensors are devices or means capable of sensing ( or responsive to ) specified measurement values and converting them into usable output signals according to certain rules. Sensors ordinarily comprise sensitive element which directly responds to the measurement values, converting element which generates output signals, and corresponding electronic circuits.
Motion sensors, as sensors having their own coordinate systems, are capable of converting the motion signals of an object into detectable electrical signals, such as the acceleration sensor and gyrocompass sensor. The acceleration sensor and gyrocompass sensor are ordinary measurement instruments for shock and vibration measurements and motion tracking in many fields such as industry and national defense, which are especially applicable in vibration measurement and motion tracking in the fields of seismology, architecture, military, transportation, machinery, navigation and the like.
The acceleration sensor is a measurement instrument for converting the physical signal of acceleration into an electrical signal which is easy to be measured. The output value of the measurement of the acceleration sensor is a voltage value reflecting the acceleration. For example, the acceleration sensor in the form of an IC chip manufactured by the Hitachi Metals Ltd, Tokyo, Japan is a three-dimentional piezoresistance acceleration sensor capable of detecting the accelerations in the three
axial directions ( X, Y and Z ). This sensor is a very small and thin three-dimensional acceleration sensor of the semiconductor type which is highly sensitive, shock-proof and pressing proof. More information relating to this acceleration sensor can be obtained from the web site http://www.hitachimetals. co.jp/e/p rod/prod 06/p06 10.htm. Those informations are incorporated herein by reference.
The gyrocompass sensor is a measurement equipment for converting the physical signal of angular velocity into electrical signal which is an easy to be measured. Similarly, the output value of measurement of the gyrocompass sensor is an electrical signal reflecting the angular velocity. In order to obtain an accurate motion locus, two or more motion sensors are ordinarly needed in a sensor system, for example, two three-dimensional motion sensors are needed in systems, such as the three-dimensional hand-writing recognition system, inertial measurement unit, robotic arm motion measurement system, aerial guidance system, appliance remote controller and the like, to sense the motion of the sensor system in the three-dimensional space. If the two or more motion sensors in a sensor system are motion sensors of the same type, for example, both of them are acceleration sensors or gyrocompass sensors, then it is necessary to calibrate the positional relationship between the coordinate systems of those two or more motion sensors, such that the output values of those two or more motion sensors in the system are transformed into the same coordinate system, so as the motion locus of the sensor system can be tracked by measuring the output values of those motion sensors.
The positional relationship between two motion sensors in a sensor system comprises a translational relationship and a rotational relationship therebetween. The translational relationship between two motion sensors is determined by the design and construction of the system electronic circuitry board, which is relatively easy to determine by measurement or other approaches. The rotational relationship between two motion sensors refers to rotating the coordinate system of one of the sensors by a specific angle required by the coordinate system of the other sensor, such that the rotational angle of the coordinate system of one of the sensors can achieve the requirements of design with respect to the coordinate system of the other sensor, for
example parallel to each other. There are two existing approaches for determining the rotational relationship between motion sensors: the first one is the approximation method, which is realized by an approximation process during the design and production of the electronic circuitry board. For example, two or more sensors are parallelly placed during the design of the electronic circuitry board, and the parallelism and freedom from rotation of the coordinate systems of the two or more sensors are realized by an as-strict-as-possible manufacturing process in their production. This approach imposes severe requirements upon the manufacturing process. The second approach is the measurement approach, in which the angles between the two or more acceleration sensors are measured by angle measurement instrument. The requirement on the measurement accuracy of the angle measurement instrument is very high in order to obtain accurate measurements.
Therefore, there is a need for a method and apparatus for rapidly, conveniently and speedily calibrating the rotational relationship between two or more motion sensors in a sensor system, for lowering the manufacturing technological requirements of the sensor systems, and for reducing the dependency on the precise angle measurement instruments.
OBJECT AND SUMMARY OT THE INVENTION It is an object of the present invention to provide a method of calibrating the rotational relationship between a first motion sensor and a second motion sensor in a sensor system, comprising the steps of: determining a minimal number of measurements based on the number of dimensions of the coordinate system of said first motion sensor and the number of dimensions of the coordinate system of said second motion sensor; measuring said sensor system for a specific number of measurements to obtain the output values of said first motion sensor and said second motion sensor during each of the measurements, said specific number of measurements is not less than said minimal number of measurements; and obtaining a rotational relationship between said first motion sensor and said second motion sensor based on said measured output values.
Since there are systematic errors and observational errors, therefore, a specific
number of measurements are carried out on said sensor system, such that the influeuce on the calibration caused by the systematic errors and the observational errors can be reduced by increasing the number of measurements to a number greater than the minimal number of measurements, and a more accurate calibration result can be achieved. According to an embodiment of the present invention, where the number of measurements is greater than the minimal number of measurements, the rotational relationship between the first motion sensor and the second motion sensor is obtained as follows: obtaining the residual error in a reference coordinate system of the output values of the first motion sensor and the second motion sensor, and obtaining the rotational relationship by processing the residual error according to an optimized strategy.
It is another object of the present invention to provide a calibration apparatus for calibrating the rotational relationship between a first motion sensor and a second motion sensor in a sensor system, the apparatus comprises: a determining means for determining a minimal number of measurements based on the number of dimensions of the coordinat system of said first motion sensor and the number of dimensions of the coordinate system of said second motion sensor; a measuring means for measuring said sensor system for a specific number of measurements to obtain the output values of said first motion sensor and said second motion sensor during each of the measurements, said specific number is not less than said minimal number of measurements; and an acquisition means for obtaining the rotational relationship between said first motion sensor and said second motion sensor based on said measured output values.
It is yet another object of the present invention to provide a computer program product for calibrating the rotational relationship between a first motion sensor and a second motion sensor in a sensor system, said computer program comprises: code for determining a minimal number of measurements based on the number of dimensions of the coordinate system of said first motion sensor and the number of dimensions of the coordinate system of the second motion sensor; code for performing a specific number of measurements on said sensor system to obtain the output values of said first motion sensor and said second motion sensor during each of the measurements,
said specific number is not less than said minimal number of measurements; and code for obtaining the rotational relationship between said first motion sensor and said second motion sensor based on said measured output ralues.
It is still another object of the present invention to provide a motion tracking system for obtaining the motion locus of the system, said system comprises at least a first motion sensor and a second motion sensor, and further comprises a calibration apparatus according to the present invention for calibrating the rotational relationship between the coordinate system of said first motion sensor and the coordinate system of said second motion sensor, and a motion tracking means for obtaining the motion locus of said first motion sensor and said second motion sensor according to the rotational relationship between the coordinate system of said first motion sensor and the coordinate system of said second motion sensor.
Other objects and effects of the present invention will be more obvious and understandable with reference to the description of the accompanying figures and the contents of the claims, and by following a more comprehensive understanding of the present invention.
BRIEF DESCRIPTION OF THE DRAWINGS
The present invention and the advantages thereof will be further elucidated with reference to the exemplary embodiments and the attached drawings, wherein:
Fig. 1 is a flow chart showing the method of calibrating the rotational relationship of two motion sensors in a calibration sensor system according to the present invention;
Fig. 2 is a schematic diagram showing an apparatus for calibrating the rotational relationship of two motion sensors in a sensor system according to the present invention; and
Fig. 3 is a schematic diagram showing a motion tracking system according to the present invention.
Like features are denoted by like reference signs throughout the drawings.
DETAILED DESCRIPTION OF THE INVENTION
Fig. 1 shows a flow chart of the method of calibrating the rotational relationship of two motion sensors in a sensor system according to the present invention.
In this embodiment, the two motion sensors in the sensor system are both acceleration sensors having three dimensional coordinate system. Let one of the two acceleration sensor be the first sensor and the another acceleration sensor the second sensor.
Firstly, a specific number of measurements of the output values of the two motion sensors in the sensor system is determined (SI lO). According to the basic principles of geometry, if both the coordinate system of the first sensor and the coordinate system of the second sensor are unidimensional coordinate systems, the rotational relationship between those two sensors can be obtained by measuring at least one set of output values of the sensors. If both the coordinate system of the first sensor and the coordinate system of the second sensor are two-dimensional coordinate systems, the rotational relationship between those two sensors can be obtained by measuring at least one sets of output values of the sensors. If both the coordinate system of the first sensor and the coordinate system of the second sensor are three-dimensional coordinate systems, the rotational relationship between those two sensors can be obtained by measuring at least three sets of output values of the sensors. In this embodiment, both the coordinate system of the first sensor and the coordinate system of the second sensor are three-dimensional coordinate systems, thus the minimal number of measurements is 3. In order to reduce the systematic errors and observational errors, the specific number of measurements is greater than 3. Secondly, the acceleration of the first sensor and the acceleration of the second sensor are measured (S 120). The acceleration of the sensor system is rendered unchanged during measurement, that is, the accelerations of the first sensor and the second sensor are measured, respectively, during static or parallelly translation period of the sensor system. It is relatively difficult to keep the sensor system in the parallelly translation state and perform measurement, and by comparision, it is relatively easy to realize the static measurement condition.
Further, the residual error in one reference coordinate system of the accelerations of the first sensor and the second sensor during this measurement is obtained (S 130). Under the condition of the static or parallelly translation state of the sensor system, the difference in the same coordinate system between the acceleration of the first sensor and the acceleration of the second sensor equals to zero, the acquirement of the rotational relationship between said coordinate systems can be realized by calculating the residual error in one reference coordinate system between the acceleration of the first sensor and the acceleration of the second sensor. The reference coordinate system can be the coordinate system of the first sensor or the coordinate system of the second sensor, or it can be the world coordinate system as well. In this embodiment, the coordinate system of the first sensor is taken as the reference coordinate system to acquire the residual error between the accelerations of the two sensors. Let ao,, and ai,, be the accelerations of the first sensor and the second sensor, respectively, in the ith measurement, then the residual error in the coordinate system of the first sensor between the acceleration of the first sensor and the acceleration of the second sensor in the ith measurement is ao,, - Rai,, .
Then, it is determined whether the number of measurements has reached the specific number (S 140). If the number of measurements is less than the specific number of measurements, the measurements of the accelerations of the first sensor and the second sensor continue. Let the sensor system be in different attitude during each of the measurements. If the measurements are made in the static state of the sensor system, the attitude of the sensor system is changed at the beginning of each new measurement; if the measurements are made in the parallel translation of the sensor system, the attitudes of the sensor system in the measurements are different from one another with respect to the world coordinate system.
If the number of measurements has reached the determined number of measurements, then the rotational relationship between the coordinate systems of the first sensor and the second sensor is obtained under the rule of sum of squares of the residual errors being minimum (S 150). Let R be the parameter of the rotational relationship between the first sensor and the second sensor, and this parameter can be expressed by a orthogonal matrix of
parameters. While R is a 3 x 3 matrix of 9 variables, however, R is a matrix of only three degrees of freedom since R is a orthogonal matrix of parameters.
According to Euler theorem, any rotation can be expressed by three rotational angles called Euler's angles. The rotational relationship between the first sensor and the second sensor can also be expressed by an Euler's angle. According to the X axis rule, a rotation can be expressed by the three Euler's angles (φ, θ, ψ): the first angle of rotation, φ, is the angle of rotation around the Z axis; the second angle of rotation, θ e [0, π], is the angle of rotation around the X axis; and the third angle of rotation, ψ, is the angle of rotation further around the Z axis. R can be expressed by R=BCD, where B, C and D are each a matrix of rotation.
Thereby, B, C and D can be expressed as follows by the use of the Euler's angles:
co&φ wnψ 0
—
mn ώ oos cii 0
0 0 1
1 0 0 0 cosø sin θ
cos φ sin^'; 0
B — gint^ cas-φ (J
0 0 1
Appropriate Euler's angles (φ, θ, ψ) can be found with the method of searching, such that the sum of squares of the residual errors of the accelerations of two sensors n in the coordinate system of the first sensor is minimum, i.e. min /J| fl0, ~ ^a \ ι Il •
The acquisition of this Euler's angle makes it possible to transform the coordinate system of the second sensor to the coordinate system of the first sensor, it can also transform the coordinate system of the first sensor to the coordinate system of the second sensor, and it can further transform the coordinate system of the first sensor
and the coordinate system of the second sensor to the world coordinate system. In summary, the acquisition of the Euler's angle can transform the coordinate system of the first sensor and the coordinate system of the second sensor to the same coordinate system.
In the above embodiment, if both the coordinate system of the first sensor and the coordinate system of the second sensor are two dimensional coordinate system, the rotational relationship between the two sensors can also be expressed by the orthogonal matrix of parameters R. Although R is a 2x2 matrix of four variables, however, R is a orthogonal matrix of parameters, thus R is a matrix of only one
cosθ sinθ degree of freedom. R can be expressed as R= . If the number of - sin θ cos θ
measurements is greater than one, when the sum of squares of the residual errors of the accelerations of the two sensors in the coordinate system of the first sensor is minimum, a more optimized value of R can be obtained.
In the above embodiment, if both the coordinate system of the first sensor and that of the second sensor are uni-dimensional coordinate systems, the measurement values of the sensors are the projections of their accelerations on the direction of their coordinate systems, and for the same acceleration, the measurement values of the two sensors are in a certain (fixed) proportion with each other. Let R be the coefficient of proportion between the measurement values of the first sensor and the measurement values of the second sensor, where R is a real number. Let A0 be the measured acceleration of the first sensor, and Ai be the measured acceleration of the second sensor. They are expressed in the form of matrix as follows:
A = , where ao,i and ai;1 represent the output values of the two
The rotational relationship between the two sensors is obtained under the rule of the sum of the squares of the residual errors of the accelerations of the two sensors in the coordinate system of the first sensor being minimum, i.e.
m}n Z^ \\ aoj - Raii ι=l
Let E=A0-RA1 (1), the problem becomes min E E (2),
it can be obtained from (2) that dETE
= 0 (3), δR
In the above embodiment, if the number of dimensions of the coordinate system of the first sensor is different from that of the second sensor, then the minimal number of measurements is determined by the small number of dimensions of the coordinate system in those two coordinate systems. Because the manufacturing cost of the motion detecting system can be greatly increased by the inconsistency of the numbers of dimensions of the coordinate systems of two sensors, there fore, in practical applications, the numbers of dimensions of the coordinate systems of the first and the second sensor are equal in most situations.
In the above embodiment, if a plurality of motion sensors exist (more than three motion sensors), the coordinate system of one of those motion sensors can be taken as the reference one, and the rotational relationships between each of the other motion sensors and this reference motion sensor can be calibrated, respectively, by the use of the above mentioned method. Thus, the rotational relationships among the coordinate systems of a plurality of motion sensors can be determined. Fig. 2 is a schematic diagram showing an apparatus for calibrating the
rotational relationship of two motion sensors in a sensor system according to the present invention. The two motion sensors in this embodiment are both three-dimensional acceleration sensor. The calibration apparatus 200 comprises: a determining means 210 for determining the minimal number of measurements based on the numbers of dimensions of the coordinate system of said first sensor and the coordinate system of said second sensor; a measuring means 220 for measuring said sensor system for a specific number of measurements to obtain the accelerations of said first motion sensor and said second motion sensor during each measurement, said specific number being not less than said minimal number of measurements; and an acquisition means 230 for obtaining the rotational relationship between said first motion sensor and said second motion sensor based on said measured accelerations.
In this embodiment, the coordinate system of the first sensor and that of the second sensor are both three-dimensional, and the determining that means determines at least three measurements are needed. The measuring means 220 is used for measuring said sensor system for the specific number of measurements to obtain the accelerations of said first motion sensor and said second motion sensor during each of the measurements, the accelerations are three-dimensional, and said specific number is not less than said minimal number of measurements (3), i.e., the specific number is equal to or greater than 3.
When the specific number of measurements is equal to 3, the acquisition means 230 acquires directly the rotational relationship between the first motion sensor and the second motion sensor based on the three sets of accelerations of the sensors measured by the measuring means 220. As stated previously, the rotational relationship between the first sensor and the second sensor can be expressed by a orthogonal matrix of three degrees of freedom, that is, it can be expressed by the Euler's angles (φ,θ,ψ). Those Euler's angles can be calculated based on the measured three sets of accelerations of the first sensor and the second sensor, and the rotational relationship between the first motion sensor and the second motion sensor can thus be obtained, while the coordinate system of the first motion sensor and that of the second motion sensor are transformed into the same coordinate system.
When the specific number of measurements is greater than 3, the acquisition means 230 comprises a residual error acquisition means 232 and an optimized processing means 234. The residual error acquisition means 232 is used for acquiring the residual errors of the accelerations of the first sensor and that of the second sensor in one reference coordinate system. The optimized processing means 234 is used to obtain the rotational relationship by processing said residual errors based on an optimized strategy. Said strategy can be: the sum of the squares of the residual errors of the output values of the first motion sensor and the second motion sensor is minimum; the sum of the absolute values of the residual errors of the output values of the first motion sensor and the second motion sensor is minimum; or the weighted sum of the residual errors of the output values of the first motion sensor and the second motion sensor is minimum.
The present invention can also be implemented by an appropriately programmed computer, with a computer program installed on the computer, that can be a computer program product for calibrating the rotational relationship between a first motion sensor and a second motion sensor in a sensor system, the computer program comprises: code for determining a minimal number of measurements based on the number of dimensions of the coordinate system of said first motion sensor and the number of dimensions of the coordinate system of said second motion sensor; code for measuring said sensor system for a specific number of measurements to obtain the output values of said first motion sensor and said second motion sensor during each of the measurements, said specific number being not less than said minimal number of measurements; and code for acquiring the rotational relationship between said first motion sensor and said second motion sensor based on said measured output values. This computer program product can be stored on a storage carrier.
This portion of program code can be provided to a processor to form a machine, such that the code executed on the processor becomes an apparatus for implementing the above mentioned functionality. Fig. 3 is a schematic diagram showing a motion tracking system according to the present invention. The motion tracking system 300 comprises two motion sensors,
a first motion sensor 310 and a second motion sensor 311. The system further comprises: a calibrating means 200, and a motion tracking means 400 for acquiring the motion locus of the motion tracking system 300 based on the rotational relationship between the coordinate system of said first motion sensor and the coordinate system of said second motion sensor.
The calibrating means 200 is used to calibrate the rotational relationship between said first motion sensor and said second motion sensor. The calibrating means 200 receives the output values of the first motion sensor 310 and the second motion sensor 320, obtains the rotational relationship of those two motion sensors, and then transmits the obtained rotational relationship to the motion tracking means
400.
The motion tracking means 400 is used to obtain the motion locus of said first motion sensor and said second motion sensor based on the rotational relationship between the coordinate system of said first motion sensor and that of said second motion sensor. When the calibrating means 200 has completed calibration, the motion tracking means 400 receives the output values of the first motion sensor 310 and the second motion sensor 320, and transforms the output values of the first motion sensor and the second motion sensor to the same coordinate system for performing motion tracking based on the rotational relationship between the coordinate system of said first motion sensor and the coordinate system of said second motion sensor.
It should be noted that the above mentioned embodiment is explanatory only rather than to limit the present invention. Those skilled in the art are capable of designing many alternative embodiments without departing from the scope of the appended claims. In the claims the reference signs in the parentheses shall not be understood as to limit the claims. The word "comprise" does not exclude other means or steps not listed in the claims. The article "a" preceding a component does not exclude the existence of a plurality of such components. The present invention can be implemented by hardware in-cluding several specific components, as well as by an appropriately programmed computer.
Claims
1. A method of calibrating the rotational relationship between a first motion sensor and a second motion sensor in a sensor system, comprising the steps of: a. determining a minimal number of measurements based on the number of dimensions of the coordinate system of said first motion sensor and the number of dimensions of the coordinate system of said second motion sensor; b. measuring said sensor system for a specific number of measurements to obtain the output values of said first motion sensor and said second motion sensor during each of the measurements, said specific number of measurements is not less than said minimal number of measurements; and c. obtaining the rotational relationship between said first motion sensor and said second motion sensor based on said measured output values.
2. The calibrating method according to claim 1 , wherein said number of dimensions of the coordinate system of the first motion sensor is one of uni-dimension, two-dimension or three-dimension, and said number of dimensions of the coordinate system of the second motion sensor is one of uni-dimension, two-dimension or three-dimension.
3. The calibrating method according to claim 1, wherein said first motion sensor and said second motion sensor are acceleration motion sensors.
4. The calibrating method according to claim 1 , wherein said first motion sensor and said second motion sensor are gyrocompass motion sensors.
5. The calibrating method according to claim 1 , wherein the attitude of said sensor system is different during each of the measurements in step (b).
6. The calibrating method according to any one of claims 1 -5, wherein said specific number of measurements is greater than said minimal number of measurements, and wherein step (c) further comprising: obtaining the residual errors of said output values in one reference coordinate system; and processing said residual errors according to an optimized strategy to obtain the rotational relationship between said first motion sensor and said second motion sensor.
7. The calibrating method according to claim 6, wherein said optimized strategy is that the sum of the squares of said residual errors is minimum.
8. A calibration apparatus for calibrating the rotational relationship between a first motion sensor and a second motion sensor in a sensor system, comprising: a. a determining means for determining a minimal number of measurements based on the number of dimensions of the coordinate system of said first motion sensor and the number of dimensions of the coordinate system of said second motion sensor; b. a measuring means for measuring said sensor system for a specific number of measurements to obtain the output values of said first motion sensor and said second motion sensor during each of the measurements, said specific number is not less than said minimal number of measurements; and c. an acquisition means for obtaining the rotational relationship between said first motion sensor and said second motion sensor based on said measured output values.
9. The calibrating apparatus according to claim 8, wherein said acquisition means comprising: a residual error acquisition means for acquiring the residual errors of said output values in one reference coordinate system; and an optimized processing means for obtaining said rotational relationship by processing said residual errors according to an optimized strategy.
10. A computer program product for calibrating the rotational relationship between a first motion sensor and a second motion sensor in a sensor system, the computer program comprising: a. code for determining a minimal number of measurements based on the number of dimensions of the coordinate system of said first motion sensor and the number of dimensions of the coordinate system of said second motion sensor; b. code for performing specific number of measurements on said sensor system to obtain the output values of said first motion sensor and said second motion sensor during each of the measurements, said specific number is not less than said minimal number of measurements; and c. code for obtaining the rotational relationship between said first motion sensor and said second motion sensor based on said measured output values.
11. A storage carrier including the computer program product according to claim 10.
12. A motion tracking system comprising at least a first motion sensor and a second motion sensor, further comprising: a calibration apparatus according to claim 8 for calibrating the rotational relationship between a first motion sensor and a second motion sensor in a sensor system; and a motion tracking means for obtaining the motion locus of said sensor system based on the rotational relationship between the coordinate system of said first motion sensor and the coordinate system of said second motion sensor.
Priority Applications (3)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CNA2005800282327A CN101006346A (en) | 2004-08-17 | 2005-08-10 | Method and apparatus for calibration |
| JP2007526671A JP2008510159A (en) | 2004-08-17 | 2005-08-10 | Method and apparatus for calibrating the rotational relationship of two motion sensors in a sensor system |
| EP05773403A EP1782076A1 (en) | 2004-08-17 | 2005-08-10 | Method and apparatus for calibrating the rotational relationship between two motion sensors of a sensor system |
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN200410055499.2 | 2004-08-17 | ||
| CNA2004100554992A CN1737580A (en) | 2004-08-17 | 2004-08-17 | Correction method and apparatus |
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| US11/573,455 A-371-Of-International US8406607B2 (en) | 2004-08-12 | 2005-08-09 | Selection of content from a stream of video or audio data |
| US13/778,439 Continuation US9143718B2 (en) | 2004-08-12 | 2013-02-27 | Method and apparatus for selection of content from a stream of data |
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| WO2006018791A1 true WO2006018791A1 (en) | 2006-02-23 |
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Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| PCT/IB2005/052643 WO2006018791A1 (en) | 2004-08-17 | 2005-08-10 | Method and apparatus for calibrating the rotational relationship between two motion sensors of a sensor system |
Country Status (5)
| Country | Link |
|---|---|
| EP (1) | EP1782076A1 (en) |
| JP (1) | JP2008510159A (en) |
| KR (1) | KR20070043009A (en) |
| CN (2) | CN1737580A (en) |
| WO (1) | WO2006018791A1 (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP1970005A1 (en) * | 2007-03-15 | 2008-09-17 | Xsens Technologies B.V. | A system and a method for motion tracking using a calibration unit |
| CN103207666A (en) * | 2012-01-16 | 2013-07-17 | 联想(北京)有限公司 | Processing method and electronic equipment for responding to operation of user |
| CN111351487A (en) * | 2020-02-20 | 2020-06-30 | 深圳前海达闼云端智能科技有限公司 | Clock synchronization method and device of multiple sensors and computing equipment |
Families Citing this family (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP6168279B2 (en) * | 2013-02-15 | 2017-07-26 | セイコーエプソン株式会社 | Analysis control device, motion analysis system, program, recording medium, and orientation adjusting method |
| CN105056503B (en) * | 2015-07-28 | 2017-09-22 | 湖南人文科技学院 | A kind of javelin mapping of training, scaling method |
| CN106226556B (en) * | 2016-07-06 | 2020-07-10 | 深圳市元征科技股份有限公司 | Acceleration sensor calibration method and device |
| CN106092141B (en) * | 2016-07-19 | 2019-03-01 | 纳恩博（常州）科技有限公司 | A kind of method and device improving relative position sensor performance |
| US20190090781A1 (en) * | 2017-09-28 | 2019-03-28 | Vital Connect, Inc. | Sensor calibration considering subject-dependent variables and/or body positions |
| CN111324172B (en) * | 2018-12-13 | 2021-11-23 | 北京小米松果电子有限公司 | Remote rod calibration method and device, electronic equipment and storage medium |
| CN110125982B (en) * | 2019-05-29 | 2020-09-25 | 北京工业大学 | Method for measuring motion trajectory orthogonality of three-degree-of-freedom motion control system of micro-operation robot |
| EP3771404A1 (en) * | 2019-07-31 | 2021-02-03 | Koninklijke Philips N.V. | Calibrating a sensor |
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| US4749157A (en) * | 1986-08-18 | 1988-06-07 | Hughes Aircraft Company | Spacecraft accelerometer auto-alignment |
| US4869092A (en) * | 1986-12-18 | 1989-09-26 | Office National D'etudes Et De Recherches Aerospatiales | Device for calibrating ultra-sensitive accelerometers |
| US20020103610A1 (en) * | 2000-10-30 | 2002-08-01 | Government Of The United States | Method and apparatus for motion tracking of an articulated rigid body |
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- 2004-08-17 CN CNA2004100554992A patent/CN1737580A/en active Pending
-
2005
- 2005-08-10 JP JP2007526671A patent/JP2008510159A/en not_active Withdrawn
- 2005-08-10 EP EP05773403A patent/EP1782076A1/en not_active Withdrawn
- 2005-08-10 KR KR1020077003869A patent/KR20070043009A/en not_active Application Discontinuation
- 2005-08-10 WO PCT/IB2005/052643 patent/WO2006018791A1/en not_active Application Discontinuation
- 2005-08-10 CN CNA2005800282327A patent/CN101006346A/en active Pending
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4749157A (en) * | 1986-08-18 | 1988-06-07 | Hughes Aircraft Company | Spacecraft accelerometer auto-alignment |
| US4869092A (en) * | 1986-12-18 | 1989-09-26 | Office National D'etudes Et De Recherches Aerospatiales | Device for calibrating ultra-sensitive accelerometers |
| US20020103610A1 (en) * | 2000-10-30 | 2002-08-01 | Government Of The United States | Method and apparatus for motion tracking of an articulated rigid body |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP1970005A1 (en) * | 2007-03-15 | 2008-09-17 | Xsens Technologies B.V. | A system and a method for motion tracking using a calibration unit |
| CN103207666A (en) * | 2012-01-16 | 2013-07-17 | 联想(北京)有限公司 | Processing method and electronic equipment for responding to operation of user |
| CN111351487A (en) * | 2020-02-20 | 2020-06-30 | 深圳前海达闼云端智能科技有限公司 | Clock synchronization method and device of multiple sensors and computing equipment |
Also Published As
| Publication number | Publication date |
|---|---|
| CN1737580A (en) | 2006-02-22 |
| KR20070043009A (en) | 2007-04-24 |
| JP2008510159A (en) | 2008-04-03 |
| EP1782076A1 (en) | 2007-05-09 |
| CN101006346A (en) | 2007-07-25 |
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