Abstract: In order to provide an inertial sensor capable of suppressing a wrong diagnosis even in an adverse environment such that sudden noise occurs, an inertial sensor is provided with a movable part (105), a first detection unit (C1, C2) for detecting the amount of displacement of the movable part (105), a forced vibration means (503, C3, C4) for forcedly vibrating the movable part (105) by applying a diagnosis signal, a physical quantity calculation unit (502) for calculating the physical quantity from a detection signal from the first detection unit (C1, C2), and an abnormality determination unit (504) for determining the presence or absence of the abnormality for the physical quantity using the diagnosis signal obtained via the first detection unit (C1, C2), and is used within a vehicle, the inertial sensor further comprising a second sensor (510) mounted in the same vehicle and connected to the abnormality determination unit (504).

Abstract: Disclosed herein are a device for detecting motions and a method for detecting motions. The device for detecting motions includes a sensor detecting motions to output detection result signals; an accumulation operation unit accumulatively summing absolute values of the detection result signals in a preset accumulation period to derive signal accumulation values; a motion determination unit comparing the signal accumulation values with a preset first reference value to determine whether the motions are present; and an output unit outputting motion detection signals according to determination results of the motion determination unit. By this configuration, the exemplary embodiments of the present invention can reflect a size of the detection result signals to motion detection while improving inaccuracy of the motion detection according to a fixing of a threshold value.

Abstract: Techniques for system-based motion detection is described, including a first accelerometer configured to detect a first acceleration associated with a system element, a second accelerometer configured to detect a second acceleration associated with the system, and a differential amplifier configured to generate a signal corresponding to the first acceleration, wherein the signal is used to distinguish the first acceleration from the second acceleration.

Abstract: A smart sensor circuit board comprises an interface to a wireless smart sensor board platform, a multi-axis accelerometer having a sensitivity that can measure ambient structural vibrations resulting from non-catastrophic routine environmental factors, an analog to digital converter (ADC) for converting signals from the multi-axis accelerometer having a plurality of individual channels including oversampling, filtering, and decimation, and each channel being individually programmable for gain, anti-aliasing, cut-off frequency, sampling, and frequency providing data to the interface, and a low noise and high sensitivity amplifier having the plurality of individual channels to receive signals from the multi-axis accelerometer.

Abstract: Systems and methods for determining states and state changes on a personal wireless device, and triggering actions upon these state changes. The personal wireless device includes at least a user interface, a positioning system and a system to determine the device acceleration. Examples of these systems are an accelerometer to determine the device acceleration and GPS (Global Positioning System) to determine the device position. States incurred from user movement include, but are not limited to: walking, driving, stationary. In one embodiment, the location of a parked vehicle is automatically saved, and a user interface to display past parking locations and guide the user to one of these parking locations, is offered.

Abstract: A accelerometer includes a substrate define a stationary electrode thereon, a first moveable mass defining a conductive-layer thereon facing the stationary electrode, a plurality of first elastic elements coupled with a peripheral side of the first moveable mass, a first fixed element surrounding the first moveable mass and fixedly attached to the substrate, a plurality of first fixed electrodes extending outwardly from the first fixed element, a second moveable mass surrounding the first fixed electrodes, a plurality of first moveable electrodes extending inwardly from the second moveable mass toward the first fixed element and parallel to the first fixed electrodes, respectively, a plurality of second elastic elements coupled with a peripheral side of the second moveable mass, and a second fixed element surrounding the second moveable mass and fixedly attached to the substrate.

Abstract: An output circuit that occupies a small area includes a control unit, X, Y, and Z axes amplification units, and first and second common circuits. The control unit outputs a temperature coefficient offset for correcting the temperature dependence of a sensor output. The first and second common circuits use the output from an acceleration sensor when performed amplification for each axis. In a reset phase, the charge accumulated in the first and second common circuits is released. In an amplification phase, the first and second common circuits and an operational amplifier uses the temperature coefficient offset voltage of each voltage to correct and amplify a signal from the acceleration sensor. In a hold phase, the accumulated charge is maintained in the same state to hold the output value of each axis.

Abstract: A MEMS multiaxial inertial sensor of angular and linear displacements, velocities, or accelerations has four comb drive capacitive sensing elements integrated on a planar substrate, each sensing element having an output responsive to displacement along a Z axis, and responsive to a displacement along X or Y axes. The sensing elements are located at different parts of the substrate on both sides of the X axis and the Y axis, the outputs being suitable for subsequently deriving linear and angular displacements about any of the X, Y or Z axes. Linear or angular movement is determined from combinations of the sensor signals.

Abstract: A method and a system for motion tracking, capable of tracking a trajectory of a movable object by an architecture having at least three accelerometers arranged in a predefined structure. The trajectory, displacement and rotational angle of the movable object are determined by ways of extrapolation, numerical calibration and vector transformation according to the acceleration signals detected by the at least three accelerometers.

Abstract: An sensor device with high detection accuracy. A time-point measurement unit is provided for measuring time-point information and adding the time-point information to an angular velocity sensing signal and an acceleration sensing signal. The angular velocity sensing signal and the acceleration sensing signal are linked by the time-point information. This structure enables output of the angular velocity sensing signal and the acceleration sensing signal linked by the time-point information. Accordingly, the angular velocity sensing signal can be accurately corrected using the acceleration sensing signal. The detection accuracy of the sensor device thus improves.

Abstract: Provided is a device for detecting a double motion and a method of detecting a double motion. The device includes a sensor configured to detect a motion; a variation rate calculating part configured to calculate a variation rate of a signal output from the sensor; a detecting section control part configured to control a detecting section in reverse proportion to a value; a first motion detecting part and a second motion detecting part configured to determine that a motion occurs; and an output part configured to output a double motion result when a time between a time (t1) and a time (t2), and to output a single motion result when the time between the time (t1) and the time (t2) is larger than the detecting section. Therefore, it is possible to adjust the detecting section to the double motion according to the motion velocity.

Abstract: A sensor element is provided for sensing accelerations in three spatial directions, which furnishes reliable measurement results and moreover can be implemented economically and with a small configuration. The sensor element encompasses at least one seismic mass deflectable in three spatial directions, a diaphragm structure that functions as a suspension mount for the seismic mass, and at least one stationary counterelectrode for capacitive sensing of the deflections of the diaphragm structure. According to the exemplary embodiments and/or exemplary methods of the present invention, the diaphragm structure encompasses at least four electrode regions, electrically separated from one another, that are mechanically coupled via the seismic mass.

Abstract: An acceleration sensor includes a substrate and a first mass element, which is connected to the substrate in such a way that the first mass element is rotatable about an axis, the first mass element being connected to a second mass element in such a way that the second mass element is movable along a first direction parallel to the axis, and the first mass element being connected to a third mass element in such a way that the third mass element is movable along a second direction perpendicular to the axis.

Abstract: In a method for operating a sensor system including a substrate having a main plane of extension and an oscillating structure which is movable relative to the substrate, drive elements excite the oscillating structure to a torsional oscillation about an axis of oscillation running essentially perpendicular to the main plane of extension, first detection elements detect a first tilting movement of the oscillating structure about a first tilting axis essentially parallel to the main plane of extension, and further detection elements detect an angular acceleration of the substrate superposed to the torsional oscillation essentially about the axis of oscillation.

Abstract: An acceleration sensor includes a substrate, a rocker mass, a z spring connected to the rocker mass, which allows the rocker mass to rotate about an axis, and at least one additional spring system connected to the substrate and the rocker mass. The additional spring system allows the rocker mass to deflect in an x or y direction oriented parallel or perpendicular to the axis. The z spring or the additional spring system allows the rocker mass to deflect in a y or x direction oriented parallel or perpendicular to the axis.

Abstract: A system and method for analyzing a device that includes a mass configured for motion. The system includes a tri-axial accelerometer disposed to detect acceleration vectors of the device and to output three channels of acceleration data, and a user interface receiving the three channels of acceleration data. The user interface is configured to correlate the three channels of acceleration data with a reference frame defined by three orthogonal axes intersecting at a vertex, and includes a display and a selector. The display shows sets of options that represent dispositions of the device with respect to gravity, placements of the tri-axial accelerometer with respect to the device, and orientations of the tri-axial accelerometer with respect to the device. The selector selects one device disposition option, one tri-axial accelerometer placement option, and one tri-axial accelerometer orientation option.

Abstract: The method and apparatus for tracking a center of gravity (COG) of an air vehicle provides a precise calculation and updating of the COG by disposing a plurality of acceleration measuring devices on a circumference of one or more rings in a manner that establishes redundancy in acceleration measurement. A multivariable time-space adaptive technique is provided within a high speed digital signal processor (DSP) to calculate and update the position of the COG. The system provides the capability of executing a procedure that reduces dispersion in estimating angular velocities and lateral accelerations of a moving vehicle and corrects the vehicle's estimated angular velocities and lateral accelerations. In addition, a consistency check of the measured values from the acceleration measuring devices is performed to assist in fault detection and isolation of a faulty accelerometer in the system.

Abstract: An angular rate sensor and an acceleration sensor are sealed at the same sealing pressure. The sealing pressure at this time is put into a reduced pressure state below the atmospheric pressure in view of improving a detection sensitivity of the angular rate sensor. Even in the reduced pressure atmosphere, to improve the detection sensitivity of the acceleration sensor, a shift suppressing portion (damper) for suppressing shifts of a movable body of the acceleration sensor is provided. This shift suppressing portion includes a plurality of protruding portions integrally formed with the movable body and a plurality of protruding portions integrally formed with a peripheral portion, and the protruding portions are alternately disposed separately at equal intervals.

Abstract: A method of determining at least one rotation parameter of a wind turbine rotor rotating with a rotation speed and a phase is provided. The method includes: measuring an effective centrifugal force acting in a first pre-determined direction, which is defined in a co-ordinate system rotating synchronously with the rotor, on at least one reference object located in or at the rotor, establishing a first angular frequency representing the rotation speed of the rotor on the basis of variations in the measured effective centrifugal force due to gravitational force, establishing a second angular frequency representing the rotation speed of the rotor by use of at least one yaw rate gyro, and establishing the value of the rotation speed as the rotational parameter by correcting the second angular frequency by comparing it to the first angular frequency.

Abstract: A motion detector (10) includes a chamber (102), a resilient suspension arm (104), an air bearing slider (110), at least one piezoresistive sensor (106), and an infrared sensor module (112). The chamber has a front plate (1024) and a back plate (1026) located on the opposite side of the chamber, and each of the front plate and the back plate has a first through hole (1030) and a plurality of second through hole (1032) formed therein. The resilient suspension arm is arranged in the chamber, and has a free distal end (1042). The air bearing slider is moveable coupled to the free distal end of the resilient suspension arm. The at least one piezoresistive sensor is attached on the air bearing slider. The infrared sensor module is arranged on the front plate of the chamber, for sensing infrared light.

Abstract: A projector has: light source (1R, 1G, 1B); a light modulation unit (6) that modulates a light emitted from the light source based on image signals; a display control unit (41) that outputs the image signals including main cyclic image signals to the light modulation unit, and controls the display thereof; a projection unit (7) that projects the image based on the light modulated by the light modulation unit; and an imaging unit (40) that captures an image to be displayed based on the light projected from the projection unit, and the display control unit inserts a correction image signal for projecting a correction image, which is visually recognized as a uniform white or gray screen when time integration is performed, between the cyclic main image signals.

Abstract: An instrumented ball for collecting data in an industrial mill comprising a durable sphere defining an enclosed cavity and having a substantial thickness, the sphere manufactured from a resilient material able to withstand pressures exerted by a working industrial mill, electronics disposed in the cavity comprising: a plurality of devices for sensing physical conditions inside the mill, wherein each of the sensing devices outputs a series of sensed values, the devices comprising at least an accelerometer, a gyroscope, a thermocouple, a microphone and a wear sensor, a memory for storing the sensed values, and a communication port for transmitting the sensed values to an external device located outside of the mill, and a power source disposed in the cavity for powering the electronics.

Abstract: A microelectromechanical systems (MEMS) sensor device (184) includes a sensor portion (180) and a sensor portion (182) that are coupled together to form a vertically integrated configuration having a hermetically sealed chamber (270). The sensor portions (180, 182) can be formed utilizing different micromachining techniques, and are subsequently coupled utilizing a wafer bonding technique to form the sensor device (184). The sensor portion (180) includes one or more sensors (186, 188), and the sensor portion (182) includes one or more sensors (236, 238). The sensors (186, 188) are located inside the chamber (270) facing the sensors (236, 238) also located inside the chamber (270). The sensors (186, 188, 236, 238) are configured to sense different physical stimuli, such as motion, pressure, and magnetic field.

Abstract: Disclosed herein is a selective motion recognition apparatus using an inertial sensor. The selective motion recognition apparatus using an inertial sensor includes: an sensor unit; a selection unit that outputs a sensor selection signal; and a motion detection unit that receives an angular velocity sensor data and an acceleration sensor data output from the sensor unit.

Abstract: An inertial rotation sensor including a vibrating member having facing metal-plated portions forming a variable capacitance capacitor associated with a low impedance load circuit via a multiplexer/demultiplexer member.

Abstract: An example geolocation system for mounting on a mammal incorporates simple sensing sleeves on the calves of the body support members, combined with an accelerometer based gravity direction and force sensing at the center of mass of the body. The example system is connected to a digital processing unit and a battery power supply to integrate the sensing to determine kinetic and potential energy of the body locomotion over time in a method that integrates out the aperiodic motion of the body about the center of mass, and uses the residual motion to measure the center of mass locomotion from a known point.

Abstract: A transducer (20) includes sensors (28, 30) that are bonded to form a vertically integrated configuration. The sensor (28) includes a proof mass (32) movably coupled to and spaced apart from a surface (34) of a substrate (36). The sensor (30) includes a proof mass (58) movably coupled to and spaced apart from a surface (60) of a substrate (56). The substrates (36, 56) are coupled with the surface (60) of substrate (56) facing the surface (34) of substrate (36). Thus, the proof mass (58) faces the proof mass (32). The sensors (28, 30) are fabricated separately and can be formed utilizing differing micromachining techniques. The sensors (28, 30) are subsequently coupled (90) utilizing a wafer bonding technique to form the transducer (20). Embodiments of the transducer (20) may include sensing along one, two, or three orthogonal axes and may be adapted to detect movement at different acceleration sensing ranges.

Abstract: A motion detection device includes: an acceleration detection unit, a separating unit, a gravity axis determination unit, and a motion detection unit. The acceleration detection unit detects acceleration components of each axis of a three-dimensional rectangular coordinate system of acceleration acting on the acceleration detection unit and outputs sets of acceleration component data. The separating unit separates the outputted sets of acceleration component data into stationary components and motion components. The gravity axis determination unit determines an axis whose separated stationary component is the largest to be a gravity axis. The motion detection unit detects, if an axis corresponding to a largest motion component showing a largest value of the separated motion components is an axis other than the determined gravity axis, a motion axis of the acceleration detection unit on the basis of the largest motion component.

Abstract: A device for detecting breakage of a turbomachine shaft is disclosed. The device includes a shaft having an upstream end and a downstream end; a rod having an upstream end and a downstream end, and placed coaxially inside the shaft, the downstream end of the rod being securely fastened to the downstream end of the shaft and the upstream end of the rod being free to rotate relative to the upstream and of the shaft; and a sensor suitable for detecting a difference in speed of rotation between the upstream end of the rod and the upstream end of the shaft.

Abstract: A semiconductor device according to the present invention includes a semiconductor substrate and an MEMS sensor provided on the semiconductor substrate.

Abstract: A 3-dimensional MEMS accelerometer fabricated on a single planar substrate deploys three co-planar sensor elements. Each sensor element is a capacitive device deploying a static electrode plate and a parallel dynamic electrode plate supported by a torsion beam. The dynamic electrode plate also includes a proof mass portion that displaces the center of gravity to below the plane of the plate. Two of the sensor elements are identical and rotated by 90 degrees on the planar substrate. The third capacitive sensor has two pairs of adjacent capacitive plates, each one having a dynamic electrode plate is suspended by a torsion beam. The proof mass on each dynamic electrode plates however is offset laterally from the torsion axis in opposite directions from the other plates to cancel the their respective capacitance charges induced by in-plane acceleration. However, this arrangement also adds the capacitive change induced by acceleration orthogonal to the planar substrate.

Abstract: An inertial system design approach that can sense and tolerate failures of individual single dimensional acceleration and/or rotation sensors with a minimal number of sensors. Sets of 4 single dimensional acceleration and/or rotation sensors can provide full 3 dimensional sensing in spite of a sensor malfunction or failure, and sets of 3 single dimensional acceleration and/or rotation sensors can provide full 2 dimensional sensing in spite of a sensor malfunction or failure.

Abstract: There are disclosed systems and methods for measuring the bowing parameters and the bowed string dynamics of a player playing a bowed string instrument. A system for measuring the bowing parameters and the bowed string dynamics may comprise a computer, a bow system and a base component. The bow system may comprise a force sensing mechanism and a bow board. The bow board may comprise an acceleration and angular velocity sensing mechanism, a position and speed sensing mechanism, a data communication module, and a power module. The base component may comprise an acceleration and angular velocity sensing mechanism, a position and speed sensing mechanism, a data communication module, and a power module.

Abstract: A track measurement apparatus for sports shoes includes a first accelerometer module located at a rear side of a sole of a shoe and a second accelerometer module located at a front side of the sole of the shoe to measure acceleration alterations of the shoe worn by a user in striding forwards during running, and also derive alterations of angular velocity and angle while the shoe is stridden forwards to get motion status of the shoe.

Abstract: Systems and methods for forming an electronic assembly are provided. A first inertial sensor having a first sense axis is attached to a bracket. A second inertial sensor having a second sense axis is attached to the bracket such that the second sense axis is substantially orthogonal to the first sense axis. The bracket is attached to a circuit board having at least one microelectronic device mounted thereto.

Abstract: A method of determining at least one rotation parameter of a wind turbine rotor rotating with a rotation speed and a phase is provided. The method comprises the steps of: measuring an effective centrifugal force acting in a first pre-determined direction, which is defined in a co-ordinate system rotating synchronously with the rotor, on at least one reference object located in or at the rotor, establishing a first angular frequency representing the rotation speed of the rotor on the basis of variations in the measured effective centrifugal force due to gravitational force, establishing a second angular frequency representing the rotation speed of the rotor by use of at least one yaw rate gyro, and establishing the value of the rotation speed as the rotational parameter by correcting the second angular frequency by comparing it to the first angular frequency.

Abstract: A method for measuring positional changes of an object, including rotation about any or all of three axes, using linear accelerometers. There is disclosed a method of using a linear accelerometer to integrate two 3D linear accelerometers in order to measure and supply for further use six-dimensional information, that is, translation in three dimensions and rotation about three axes. Two linear accelerometer sensors are used to determine all but rotation about an imaginary axis between the accelerometers. Output from a third accelerometer may be used to generate the data needed to determine rotation about the imaginary axis. The need for a gyroscope for detecting changes in heading (i.e., yaw or azimuth) may therefore be avoided.

Abstract: Monolithic solid-state inertial sensor. The sensor detects rotation rate about three orthogonal axes and includes a micromachined monolithic piezoelectric crystalline structure including an equal number of vibratory drive and detection tines on each side of an axis of symmetry of the sensor, the tines being synchronized to have alternate actuation movements inward and outward.

Abstract: An electronic apparatus includes an acceleration detection unit configured to detect acceleration acting on the electronic apparatus, a noise removal unit configured to remove a noise component from an output of the acceleration detection unit, a first determination unit configured to determine whether output from the noise removal unit indicates acceleration equal to or less than a first acceleration, a second determination unit configured to determine whether output from the noise removal unit indicates acceleration equal to or less than a second acceleration, and a fall state determination unit configured to determine that the electronic apparatus is falling when the first determination unit detects that output from the noise removal unit is equal to or less than the first acceleration, or when the second determination unit determines that output from the noise removal unit is equal to or less than the second acceleration.

Abstract: A combined detection element (6) of the present invention includes an acceleration detection element (2) and an angular velocity detection element (4) stacked on the acceleration detection element (2) in such a manner as to avoid contacting with the weight parts (12) of the acceleration detection element (2). The angular velocity detection element (4) includes a recess (26) in a surface thereof facing the weight parts (12) of the acceleration detection element (2) so as to avoid contacting with the weight parts (12). At least part of the recess (26) has a depth not exceeding the vertical range of motion of weight parts (12), thereby suppressing the upward movement of weight parts (12).

Abstract: A method of mounting in-plane sensors of an inertial measurement unit. The method includes the steps of: providing a structure having first and second planar surfaces oriented orthogonally to one another, positioning a plurality of sensors on the first planar surface such that each of the sensors has a sense axis extending parallel to the first planar surface, positioning at least one other sensor on the second planar surface such that the at lease one other sensor has a sense axis extending parallel to the second planar surface, and orienting the sensors on the first and second surfaces so that the angles formed between any two sense axes are equal.

Abstract: A system for estimating motion parameters corresponding to a user. The system may generally include a receiver operable to receive a signal from an external source, an inertial sensor operable to be coupled with the user and arbitrarily oriented relative to the direction of user motion for generation of a signal corresponding to user motion, and a processing system in communication with the receiver and inertial sensor.

Abstract: A motion sensing apparatus generally comprising a housing unit operable to be attached to an object at an attachment position, an accelerometer operable to provide a signal corresponding to an acceleration measurement; and a processing system. The processing system is operable to acquire the signal corresponding to the acceleration measurement and analyze the acquired acceleration measurement to identify the attachment position of the housing unit.

Abstract: A system and method in accordance with the present invention provides for a low cost, bulk micromachined accelerometer integrated with electronics. The accelerometer can also be integrated with rate sensors that operate in a vacuum environment. The quality factor of the resonances is suppressed by adding dampers. Acceleration sensing in each axis is achieved by separate structures where the motion of the proof mass affects the value of sense capacitors differentially. Two structures are used per axis to enable full bridge measurements to further reduce the mechanical noise, immunity to power supply changes and cross axis coupling. To reduce the sensitivity to packaging and temperature changes, each mechanical structure is anchored to a single anchor pillar bonded to the top cover.

Abstract: An inertial sensor includes an oscillator that is supported by an elastic supporting member such that the oscillator is floating relative to a base and the oscillator is displaceable along a single axis, and a displacement detection unit detecting a displacement of the oscillator. The oscillation of the oscillator is a simple harmonic motion along a Z axis. An X axis, a Y axis, and the Z axis, serving as reference axes of an oscillation coordinate system for the oscillator, are shifted to provide x, y, and z axes, serving as new reference axes. Position coordinates of the oscillator of the x, y, and z axes are determined in at least two points during one period of the oscillator. A difference vector (?x, ?y, ?z) is calculated on the basis of the determined position coordinates. An angular velocity or an acceleration is obtained using the difference vector.

Abstract: An angular velocity detection apparatus includes: a sensor unit having first and second detection axes serving as angular velocity detection axes, the first and second detection axes intersecting each other; a sensor output correction circuit for making at least one of an offset adjustment and a sensitivity adjustment to a detection output of an angular velocity around the first detection axis and a detection output of an angular velocity around the second detection axis; a sign determination circuit for obtaining a sign of a rotational direction of an angular velocity on any one of the first and second detection axes; and an amplitude calculation circuit for multiplying a square sum average of detection outputs of angular velocities around the first and second detection axes outputted by the sensor output correction circuit and a sign outputted by the sign determination circuit.

Abstract: In a method for determining the relative position, velocity, acceleration, and/or the rotation center of a body displaceable in a three dimensional space, at least twelve linear acceleration sensors are provided and in each case arranged on a position which is stationarily fixed with respect to the body. At least one acceleration measurement signal is captured by the linear acceleration sensors. A position, velocity, acceleration, and/or rotation center signal is generated for the body from the acceleration measurement signal and data describing the position and orientation of the linear acceleration sensors in the body-fixed coordinate system.

Abstract: An accelerometer with improved immunity to sensitivity drift is disclosed. In some embodiments, the accelerometer comprises an actuator that induces a known acceleration on a reference frame. A signal based on this known acceleration is used to calibrate the accelerometer to mitigate the effects due to at least one of sensitivity drift, D.C. bias drift, sense laser wavelength drift, and resonant frequency drift.

Abstract: An inertial measurement unit is disclosed which includes a system of gyros for sensing angular rates, a system of accelerometers for sensing angular accelerations, an integrator for deriving gyro-less angular rates from the sensed angular accelerations, and a complimentary filter for blending the sensed angular rates and the gyro-less angular rates to produce a virtual angular rate output for the inertial measurement unit.

Abstract: A method for measuring positional changes of an object, including rotation about any or all of three axes, using linear accelerometers. There is disclosed a method of using a linear accelerometer to integrate two other 3D linear accelerometers in order to measure and supply for further use six-dimensional information, that is, translation in three dimensions and rotation about three axes. Two linear accelerometer sensors are used to determine all but one of the variables in the six degrees of freedom. Output from a third accelerometer generates the data need to determine a sixth, rotational, degree of freedom. The need for a gyroscope for detecting changes in heading (i.e., yaw or azimuth) may therefore be avoided.