WO2009077976A2 - Mesure de l'orientation d'un objet - Google Patents

Mesure de l'orientation d'un objet Download PDF

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Publication number
WO2009077976A2
WO2009077976A2 PCT/IB2008/055319 IB2008055319W WO2009077976A2 WO 2009077976 A2 WO2009077976 A2 WO 2009077976A2 IB 2008055319 W IB2008055319 W IB 2008055319W WO 2009077976 A2 WO2009077976 A2 WO 2009077976A2
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WO
WIPO (PCT)
Prior art keywords
measurement
magnetic field
orientation
acceleration
processing means
Prior art date
Application number
PCT/IB2008/055319
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English (en)
Other versions
WO2009077976A3 (fr
Inventor
Victor M. G. Van Acht
Nicolaas Lambert
Edwin G. J. M. Bongers
Gerd Lanfermann
Original Assignee
Koninklijke Philips Electronics N.V.
Philips Intellectual Property & Standards Gmbh
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Koninklijke Philips Electronics N.V., Philips Intellectual Property & Standards Gmbh filed Critical Koninklijke Philips Electronics N.V.
Publication of WO2009077976A2 publication Critical patent/WO2009077976A2/fr
Publication of WO2009077976A3 publication Critical patent/WO2009077976A3/fr

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Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C17/00—Compasses; Devices for ascertaining true or magnetic north for navigation or surveying purposes
    • G01C17/02—Magnetic compasses
    • G01C17/28—Electromagnetic compasses
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • G01C21/165—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
    • G01C21/1654—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments with electromagnetic compass

Definitions

  • the invention relates to methods and systems for improving the measurement of the orientation of an object.
  • Three-dimensional accelerometers can be attached to objects, and can measure the acceleration of the object in three dimensions. As part of these measurements, the accelerometer measures forces on the object caused by gravity.
  • the accelerometer can be used as a tilt sensor to measure the angular orientation of the object relative to the horizontal.
  • orientation of an object can be measured or determined using a combination of a three-dimensional accelerometer to measure the tilt of the object and a two- or three-dimensional magnetometer that measures the Earth's magnetic field.
  • Fig. 1 shows a block diagram of a system that can measure or estimate the orientation of an object.
  • the system 2 comprises an accelerometer 4 and a magnetometer 6 that provide measurements of the acceleration and magnetic field respectively of an object to which they are attached. The measurements are denoted s A m and s M m respectively, where V indicates that the measurements are in a frame of reference that is fixed relative to the sensor or object, and 'm' indicates that these are measurements from the accelerometer or magnetometer.
  • the system 2 also comprises a register or memory 8 for storing a previous estimate of the orientation Q of the object.
  • the orientation Q may be mathematically represented as a quaternion, Euler angles or any other suitable orientation representation.
  • the basic value for the orientation Q is determined from a gyroscopic measurement (described further below), and is modified based on the measurements of the accelerometer 4 and magnetometer 6
  • a first unit 10 provides an expected measurement for acceleration on the object caused by gravity (vector G) in a world-based frame of reference.
  • This expected measurement denoted w A e (where 'w' indicates that the measurements are in a world- coordinate frame of reference and 'e' indicates that the measurement is an expected value) is provided to a first transformation unit 11 that calculates the expected measurement from the accelerometer 4 expressed in the sensor-fixed coordinate frame, based on the previous estimate Q of the orientation of the object.
  • the first transformation unit 11 converts or rotates a vector G associated with gravity in a world-based reference frame to a frame of reference that is fixed relative to the object.
  • a second unit 12 provides an expected measurement for the magnetic field (vector M) in a world-based frame of reference.
  • the expected measurement denoted w M e
  • the second transformation unit 13 that calculates the expected measurement from the magnetometer based on the previous estimate Q of the orientation of the object.
  • the second transformation unit 13 converts the vector M into the frame of reference that is fixed relative to the object.
  • a first adder 14 determines the difference between the actual measurement from the accelerometer 4 and the expected or estimated value from the first transformation unit 11.
  • a second adder 15 determines the difference between the actual measurement from the magnetometer 6 and the expected or estimated value from the second transformation unit 13.
  • the combination of the outputs of the two adders 14, 15 form an error signal or vector which is denoted s ⁇ .
  • the error vector s ⁇ is provided to a calculation block 16. As the error vector s ⁇ includes three-dimensional elements for both the acceleration and magnetic field, it will be appreciated that it is a six-dimensional vector.
  • the calculation block 16 calculates a sensitivity matrix of the estimated orientation Q to the individual error signals in the vector s ⁇ by differentiating s ⁇ to the orientation Q and taking the inverse. The calculation block 16 then multiplies the error signals s ⁇ by the sensitivity matrix to obtain a correction signal ⁇ Q for the orientation Q.
  • the correction value ⁇ Q is weighted by a factor 1/k (where k»l) in a first multiplier 18, before being provided to a first updater 20.
  • the correction value ⁇ Q is combined with the previous estimate of the orientation Q in the first updater 20 and the output of the updater 20 is provided to a second updater 22.
  • the system 2 further comprises a gyroscope 24 which provides measurements of the angular speed of the object. These measurements, denoted O m , are sampled at frequency 1/dt, and are multiplied by second multiplier 26 in order to allow for a correct integration of the angular velocity measurement with the angular orientation Q, before being combined with the output of the first updater 20 in the second updater 22. The resulting value for the orientation of the object Q is stored in the memory 8.
  • updater 22 is a multiplier, known as a quaternion multiplier.
  • updater 22 is a multiplier, known as a matrix multiplier. The process then repeats in an iterative loop.
  • the gyroscope 24 provides the main measurement used to determine the orientation of the object.
  • the accelerometer 4 and magnetometer 6 are provided to compensate for this offset.
  • the combination of the gyroscope, accelerometer and magnetometer means that the gyroscope can track fast rotations while the accelerometer and magnetometer guarantee the long-term stability of the system.
  • the cross-over frequency between the gyroscope and accelerometer and magnetometer can be tuned by changing the gain factor k.
  • an object orientation measurement system for calculating an estimate of the orientation of an object to which the system can be attached, the system comprising measurement means for taking measurements of a plurality of parameters used in calculating an estimate of the orientation of the object; and processing means for comparing a measurement of at least one of the parameters with a first predetermined value; and calculating an estimate of the orientation of the object using the measurements of the plurality of parameters, wherein the weighting of the measurement of the at least one parameter is adjusted relative to the measurement of at least one other parameter based on the result of the comparison.
  • a method for calculating an estimate of the orientation of an object comprising taking measurements of a plurality of parameters used in calculating an estimate of the orientation of the object; comparing a measurement of at least one of the parameters with a first predetermined value; and calculating an estimate of the orientation of the object using the measurements of the plurality of parameters, wherein the weighting of the measurement of the at least one parameter is adjusted relative to the measurement of at least one other parameter based on the result of the comparison.
  • an object orientation measurement system for calculating an estimate of the orientation of an object to which the system can be attached, the system comprising an accelerometer for measuring an acceleration of the object in a frame of reference that is fixed relative to the object; a magnetometer for measuring a magnetic field in the frame of reference that is fixed relative to the object; processing means for determining the azimuth angle of the magnetic field from the measurement of the magnetic field; and calculating an estimate of the orientation of the object using the measurement of the acceleration of the object and the azimuth angle of the magnetic field.
  • a method for calculating an estimate of the orientation of an object comprising measuring an acceleration of the object in a frame of reference that is fixed relative to the object; measuring a magnetic field in the frame of reference that is fixed relative to the object; determining the azimuth angle of the magnetic field from the measurement of the magnetic field; and calculating an estimate of the orientation of the object using the measurement of the acceleration of the object and the azimuth angle of the magnetic field.
  • Fig. 1 shows a conventional system for measuring the orientation of an object
  • Fig. 2 shows a system for measuring the orientation of an object according to a first aspect of the invention
  • Fig. 3 shows a system for measuring the orientation of an object according to a second aspect of the invention
  • Fig. 4 shows a system for measuring the orientation of an object according to a third aspect of the invention
  • Fig. 5 shows a system for measuring the orientation of an object according to a fourth aspect of the invention
  • Fig. 6 shows a system for measuring the orientation of an object according to a fifth aspect of the invention.
  • Fig. 7 shows a system for measuring the orientation of an object according to a sixth aspect of the invention.
  • the Earth's magnetic field not only has a component pointing along the Earth's surface to the magnetic north pole, but also a component that is perpendicular to the surface.
  • the resulting magnetic field vector will form an angle with a plane parallel to the surface of the Earth that varies with position on the Earth's surface.
  • the magnetic field vector w M e that is stored in the second unit 12 is a constant (for a given position on the Earth). However, this constant takes a different value as the position on the Earth's surface varies, which is difficult to implement successfully in an orientation measurement system.
  • the vertical component of the magnetic field i.e. the component that is perpendicular to the Earth's surface
  • the error signal s ⁇ is omitted from the error signal s ⁇ .
  • components of the system 30 that are common to the system 2 shown in Fig. 1 are given the same reference numeral, and operate in the same way, unless otherwise described below.
  • the accelerometer 4 and magnetometer 6 are switched around with the first unit 10 and second unit 12 respectively. Consequently, the first and second transformation units 11, 13 act to convert the measurements of the acceleration and magnetic field from a frame of reference that is fixed relative to the object/sensor into a non-object based (i.e. world- fixed) frame of reference.
  • the vertical component of the magnetic field can be excluded from the remainder of the calculation by filtering out the z-component of the vector. This function is performed by the filter block 32.
  • Fig. 3 shows a second aspect of the invention in which the vertical component of the magnetic field is omitted from the error signal s ⁇ .
  • components of the system 40 in Fig. 3 that are common to the system 2 shown in Fig. 1 are given the same reference numeral, and operate in the same way, unless otherwise described below.
  • a first vector product block 42 is provided between the second unit 12 and second transformation unit 13. This block 42 generates the vector product of the magnetic field estimate w M e and the gravitational vector w A e .
  • a second vector product block 44 is provided between the magnetometer 6 and the second adder 15, which generate the vector product of the measured magnetic field and the acceleration measured by the accelerometer 4.
  • the second adder 15 now calculates the difference between the vector product from the first vector product block 42 (after transformation into an object-based frame of reference) and the second vector product block 44.
  • a problem with using the Earth's magnetic field for orientation estimation is that magnetic disturbances in the environment local to the magnetometer can affect the measurements.
  • Such disturbances can, for example, occur inside buildings as a result of steel bars in the structure.
  • Some of the disturbances only cause a significant change to the vertical component of the magnetic field, which means that these disturbances can be overcome by utilising the invention shown in the first and second aspects above.
  • some disturbances cause significant variations in the magnetic field in the horizontal plane (for example those caused by steel furniture).
  • the magnitude of the magnetic field vector measured by the magnetometer 6 is examined to determine if the signal from the magnetometer 6 is unreliable, i.e. it is varying significantly from the vector expected for the magnetic field.
  • the magnitude of the magnetic field measured by the magnetometer 6 is much larger or smaller than that expected from the Earth's magnetic field (as given by the magnitude of w M e in the second unit 12)
  • the weighting of the measurements of the magnetometer 6 in the error signal s ⁇ relative to the measurements of the acceleration by the accelerometer 4 can be reduced.
  • the system 50 in Fig. 4 illustrates how this can be implemented in the system
  • a first gain unit 52 is provided between the first adder 14 and the calculation block 16.
  • the gain of the first gain unit 52 is given by a parameter IC A .
  • unit 52 is a fixed gain unit and the parameter IC A is a constant.
  • a second gain unit 54 is provided between the second adder 15 and the calculation block 16.
  • the unit 54 is a variable gain unit, which varies its gain in response to a control parameter kM.
  • This control parameter kM is derived by an arithmetic block 56 that receives the magnetic field vector w M e from the second unit 12 and the measured magnetic field vector s M m from the magnetometer 6.
  • the arithmetic block 56 calculates the magnitude of each vector, and compares the two values. If the values are not equal (i.e.
  • control parameter kM can be varied continuously or by discrete amounts based on the results of the comparison of the two values. It will also be appreciated that the fixed gain unit 52 can be omitted if the gain value for that unit is 1.
  • this aspect of the invention can alternatively be implemented by increasing the weighting of the acceleration measurements in the error signal s ⁇ , rather than by decreasing the weighting of the magnetometer measurements.
  • the first gain unit 52 will be a variable gain unit
  • the second gain unit 54 can be a fixed gain unit.
  • both gain units 52, 54 can be variable gain units, with the arithmetic block 56 controlling the gain of each unit 52, 54 so that the relative weighting of the magnetic field and acceleration measurements is adjusted appropriately.
  • Fig. 1 Another problem with the system in Fig. 1 is that large linear and angular accelerations (for example caused by acceleration or deceleration in a car or in an elevator) will result in the measured acceleration s A m having both a gravitational component and components due to the linear and angular acceleration of the sensor.
  • the magnitude of the acceleration vector measured by the accelero meter 4 is examined to determine if the signal from the accelerometer 4 is unreliable, i.e. it is varying significantly from the vector expected for acceleration due to gravity on the sensor.
  • the magnitude of the acceleration measured by the accelerometer 4 is much larger or smaller than that expected from gravity (as given by the magnitude of w A e in the first unit 10)
  • the weighting of the measurements of the accelerometer 4 in the error signal s ⁇ relative to the measurements of the magnetic field by the magnetometer 6 can be reduced.
  • the system 60 in Fig. 5 illustrates how this can be implemented in the system 2 of Fig. 1.
  • a first gain unit 62 is provided between the first adder 14 and the calculation block 16.
  • the unit 62 is a variable gain unit, which varies its gain in response to a control parameter IC A .
  • a second gain unit 64 is provided between the second adder 15 and the calculation block 16.
  • unit 64 is a fixed gain unit and the parameter IC M is a constant.
  • the control parameter IC A is derived by an arithmetic block 66 that receives the gravitational acceleration vector w A e from the first unit 10 and the measured acceleration vector s A m from the accelerometer 4.
  • the arithmetic block 66 calculates the magnitude of each vector, and compares the two values. If the values are not equal (i.e.
  • the arithmetic block 66 can output an appropriate value for the control parameter IC A , SO that the weighting of the acceleration measurement in the error signal s ⁇ is reduced. If the values are equal or differ by less than the predetermined amount, then the arithmetic block 66 will output a value for the control parameter kA that gives equal weighting to the magnetic field and acceleration measurements in the error signal s ⁇ .
  • control parameter kA can be varied continuously or by discrete amounts based on the results of the comparison of the two values. It will also be appreciated that the fixed gain unit 64 can be omitted if the gain value for that unit is 1.
  • this aspect of the invention can alternatively be implemented by increasing the weighting of the magnetic field measurements in the error signal s ⁇ , rather than by decreasing the weighting of the acceleration measurements.
  • the second gain unit 64 will be a variable gain unit
  • the first gain unit 62 can be a fixed gain unit.
  • both gain units 62, 64 can be variable gain units, with the arithmetic block 66 controlling the gain of each unit 62, 64 so that the relative weighting of the magnetic field and acceleration measurements is adjusted appropriately.
  • the acceleration measured by the accelerometer 4 can also include centrifugal components if the sensor is rotating. Again, this will result in the measured acceleration s A m having both a gravitational component and components due to the centrifugal force on the sensor.
  • the measurements of the angular speed by the gyroscope 24 are examined to determine if the object is experiencing rotation (i.e. the angular speed measurements are non-zero or substantially above zero), and if so, the weighting of the measurements of the accelerometer 4 in the error signal s ⁇ relative to the measurements of the magnetic field by the magnetometer 6 can be reduced.
  • the system 70 in Fig. 6 illustrates how this can be implemented in the system 2 of Fig. 1.
  • a first gain unit 72 is provided between the first adder 14 and the calculation block 16.
  • the unit 72 is a variable gain unit, which varies its gain in response to a control parameter IC A .
  • a second gain unit 74 is provided between the second adder 15 and the calculation block 16.
  • unit 74 is a fixed gain unit and the parameter k M is a constant.
  • the control parameter kA is derived by an arithmetic block 76 that receives the angular speed measurements O m from the gyroscope 24 and determines whether the angular speed is greater than zero, or greater than zero by more than a predetermined amount. If the angular speed is greater than zero, then the arithmetic block 76 can output an appropriate value for the control parameter k A , so that the weighting of the acceleration measurement in the error signal s ⁇ is reduced. If the angular speed measurement is zero, then the arithmetic block 76 will output a value for the control parameter k A that gives equal weighting to the magnetic field and acceleration measurements in the error signal s ⁇ .
  • control parameter kA can be varied continuously or by discrete amounts based on the magnitude of the angular speed.
  • the fixed gain unit 74 can be omitted if the gain value for that unit is 1.
  • this aspect of the invention can alternatively be implemented by increasing the weighting of the magnetic field measurements in the error signal s ⁇ , rather than by decreasing the weighting of the acceleration measurements.
  • the second gain unit 74 will be a variable gain unit
  • the first gain unit 72 can be a fixed gain unit.
  • both gain units 72, 74 can be variable gain units, with the arithmetic block 76 controlling the gain of each unit 72, 74 so that the relative weighting of the magnetic field and acceleration measurements is adjusted appropriately.
  • the magnitude of the angular speed measurements in the x-, y- and z- directions can be considered individually.
  • the magnitude of the angular speed measurement in the x-direction (given by s x O m ) can be used to control the weighting of the accelero meter measurements in the y- and z-directions, since rotation around the x-axis does not generate centrifugal forces in the x-direction.
  • the magnitude of the angular speed measurement in the y-direction can be used to control the weighting of the accelerometer measurements in the x- and z- directions
  • the magnitude of the angular speed measurement in the z-direction can be used to control the weighting of the accelerometer measurements in the x- and y-directions.
  • the variable gain unit 72 it will be necessary for the variable gain unit 72 to receive separate control signals for each of the x-, y- and z-directions of the accelerometer measurements.
  • the measurements of the angular speed by the gyroscope 24 are examined to determine if the object is experiencing rotation speeds that are close to or above the saturation point of the gyroscope 24. If the speeds are close to or above the saturation point of the gyroscope 24, the weighting of the measurements of both the accelerometer 4 and the magnetometer 6 can be increased.
  • the system 80 in Fig. 7 illustrates how this can be implemented in the system 2 of Fig. 1.
  • a first gain unit 82 is provided between the first adder 14 and the calculation block 16.
  • the unit 82 is a fixed gain unit, with the gain being specified by a constant parameter kA.
  • a second gain unit 84 is provided between the second adder 15 and the calculation block 16.
  • unit 84 is also a fixed gain unit and the parameter k M is a constant.
  • the first multiplier 18 in Fig. 1 is replaced by a third gain unit 86.
  • the third gain unit 86 is a variable gain unit, with the gain being specified by a control parameter k.
  • the control parameter k is derived by an arithmetic block 88 that receives the angular speed measurements s O m from the gyroscope 24 and determines whether the angular speed is greater than a maximum value. If the angular speed is equal to or greater than the maximum value, then the arithmetic block 88 can output an appropriate value for the control parameter k, so that the weighting of the acceleration and magnetometer measurements is increased (i.e. k is reduced to increase the weighting). If the angular speed measurement is below the maximum value, then the arithmetic block 88 will output a value for the control parameter k that gives a normal weighting to the magnetic field and acceleration measurements.
  • control parameter k can be varied continuously or by discrete amounts based on the proximity of the angular speed to the maximum value. It will also be appreciated that the fixed gain units 82 and 84 can be omitted if the gain value for those units is 1.
  • this aspect of the invention can alternatively be implemented by increasing the weighting of both the acceleration and magnetic field measurements using the gain units 82 and 84, rather than using a third gain unit 86.
  • the first and second gain units 82, 84 will be variable gain units
  • the third gain unit 86 can be a fixed gain unit.
  • each gain unit 82, 84, 86 can be a variable gain unit, with the arithmetic block 88 controlling the gain of each unit 82, 84, 86 so that the weighting of the magnetic field and acceleration measurements is adjusted appropriately.
  • any two or more of the aspects can be combined into a single apparatus.
  • an apparatus comprising means for implementing each of the third, fourth, fifth and sixth aspects of the invention would provide significant improvements in the orientation estimate over the prior art apparatus in Fig. 1.
  • any of the above aspects of the invention shown in Figs. 2, 3, 4 and 5 can be implemented in an orientation estimation system that does not include a gyroscope (i.e. systems in which blocks 22, 24 and 26 are omitted).
  • a computer program may be stored/distributed on a suitable medium, such as an optical storage medium or a solid-state medium supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunication systems.
  • a suitable medium such as an optical storage medium or a solid-state medium supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunication systems.

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  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Physics & Mathematics (AREA)
  • Electromagnetism (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Length Measuring Devices By Optical Means (AREA)
  • Image Processing (AREA)
  • Gyroscopes (AREA)

Abstract

L'invention porte sur un système de mesure de l'orientation d'un objet pour calculer une estimation de l'orientation d'un objet auquel le système peut être fixé, le système comprenant des moyens de mesure pour prendre des mesures d'une pluralité de paramètres utilisés dans le calcul d'une estimation de l'orientation de l'objet ; et des moyens de traitement pour comparer une mesure d'au moins l'un des paramètres avec une première valeur prédéterminée ; et calculer une estimation de l'orientation de l'objet à l'aide des mesures de la pluralité de paramètres, la pondération de la mesure du ou des paramètres étant ajustée par rapport à la mesure d'au moins un autre paramètre sur la base du résultat de la comparaison.
PCT/IB2008/055319 2007-12-18 2008-12-16 Mesure de l'orientation d'un objet WO2009077976A2 (fr)

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EP07123510.5 2007-12-18
EP07123510 2007-12-18

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WO2009077976A3 WO2009077976A3 (fr) 2009-08-20

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Cited By (4)

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Publication number Priority date Publication date Assignee Title
EP2639551A1 (fr) * 2012-03-15 2013-09-18 BlackBerry Limited Procédés et dispositifs pour la détermination de l'orientation
US20130245982A1 (en) * 2012-03-15 2013-09-19 Research In Motion Limited Methods and devices for determining orientation
US20170003751A1 (en) * 2015-06-30 2017-01-05 Stmicroelectronics S.R.L. Device and method for determination of angular position in three-dimensional space, and corresponding electronic apparatus
US11656081B2 (en) * 2019-10-18 2023-05-23 Anello Photonics, Inc. Integrated photonics optical gyroscopes optimized for autonomous terrestrial and aerial vehicles

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US6014610A (en) * 1997-01-31 2000-01-11 Greenfield Enterprises, Inc Navigation system and method
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Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP2639551A1 (fr) * 2012-03-15 2013-09-18 BlackBerry Limited Procédés et dispositifs pour la détermination de l'orientation
US20130245982A1 (en) * 2012-03-15 2013-09-19 Research In Motion Limited Methods and devices for determining orientation
US9279680B2 (en) 2012-03-15 2016-03-08 Blackberry Limited Methods and devices for determining orientation
US20170003751A1 (en) * 2015-06-30 2017-01-05 Stmicroelectronics S.R.L. Device and method for determination of angular position in three-dimensional space, and corresponding electronic apparatus
US10114464B2 (en) 2015-06-30 2018-10-30 Stmicroelectronics S.R.L. Device and method for determination of angular position in three-dimensional space, and corresponding electronic apparatus
US20190018499A1 (en) * 2015-06-30 2019-01-17 Stmicroelectronics S.R.L. Device and method for determination of angular position in three-dimensional space, and corresponding electronic apparatus
US10747330B2 (en) 2015-06-30 2020-08-18 Stmicroelectronics S.R.L. Device and method for determination of angular position in three-dimensional space, and corresponding electronic apparatus
US11656081B2 (en) * 2019-10-18 2023-05-23 Anello Photonics, Inc. Integrated photonics optical gyroscopes optimized for autonomous terrestrial and aerial vehicles

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