Abstract: An electromechanical resonator including a drive electrode set having at least one pair of alternating pole interdigitated drive electrodes and including a sense electrode set having at least one pair of alternating pole interdigitated sense electrodes.

Abstract: A resonant structure comprising at least two coaxial rings, wherein adjacent coaxial rings have adjacent peripheries and are attached together by a plurality of connection structures regularly arranged along said adjacent peripheries; and wherein a first ring has a first ring portion with a first radial thickness and a second ring, portion, in a vicinity of a first connection structure, with a second radial thickness smaller than said first radial thickness.

Abstract: An angular sensor, comprising a Coriolis vibratory gyroscope (CVG) resonator, capable of oscillating along a first pair of normal n=1 modes comprising a first normal mode and a second normal mode; and a second pair of normal n=2 modes comprising a third normal mode and a fourth normal mode; the sensor further comprising one drive electrode and one sense electrode aligned along an anti-nodal axis of each mode; and a pair of bias tune electrodes aligned with an anti-nodal axis of each mode if no drive and sense electrode pair is aligned with said anti-nodal axis.

Abstract: A resonator includes an anchor, an outer stiffener ring on an outer perimeter of the resonator, and a plurality of curved springs between the anchor and the outer stiffener ring.

Abstract: A magnetometer system has a magnetometer, an interface circuit and an electronic demodulator, the interface circuit being coupled to sense electrodes disposed on the magnetometer and the demodulator being coupled to the interface circuit. Preferably, the magnetometer has a loop electrode which follows an outline of the shape of an active portion of the magnetometer and wherein the electronic demodulator has an output for driving the loop electrode of the magnetometer. Preferably, the magnetometer includes a quartz plate with flexural and thickness shear vibratory modes and wherein the flexural vibratory mode is driven, in use, into vibration by the electronic demodulator and wherein the thickness shear vibratory mode is driven, in use, into vibration by the interface circuit.

Abstract: A method for generating an output of a downhole inertial measurement unit (IMU) includes: generating a trajectory between a plurality of survey points of a planned well data as a function of time, wherein the planned well data includes a plurality of three-dimensional coordinates corresponding to the survey points of an underground planned well are used to generate a trajectory comprising a plurality of trajectory coordinates between the consecutive ones of the survey points; generating sensor data for each of the trajectory coordinates as a function of time based on the geodetic reference parameters, the generated sensor data comprising: generated accelerometer output; generated gyroscopic output; and generated magnetometer output; and outputting the generated accelerometer output; the generated gyroscopic output; and the generated magnetometer output as a function of time as a generated output of the downhole IMU.

Abstract: A resonator and/or a magnetometer has a resonating structure which is naturally resonant in at least one resonant mode, the resonating structure being significantly wider at a free end thereof than it is at a fixed end thereof, the resonating structure having at least one pair of sense electrodes disposed on opposing major surfaces of the resonating structure and having a conductive path formed as a loop, the loop being disposed near or at edges of the resonating structure so that the loop follows a path which is significantly wider at the free end of the resonating structure than it is at the fixed end of the resonating structure and wherein the at least one pair of sense electrodes are formed inwardly of the edges of the resonating structure and also inwardly of the path of the loop.

Abstract: Described is a system for estimating measured depth of a borehole. The system comprises a drilling fluid pulse telemetry system positioned in a borehole and processors connected with the drilling fluid pulse telemetry system. Time series measures are obtained from an environmental sensor package. Initial estimates of a time delay and path attenuation amplitude are determined. An error for the initial estimates is determined, and iterative minimization of the error is performed until source signal parameters converge, resulting in a least squares estimate of the source signal and the reflected signals. The least squares estimate is used to obtain time delay values, which are then used to continuously generate an estimate of a measured depth of the borehole.

Abstract: Described is a system for adaptive calibration of a sensor of an inertial measurement unit. Following each sensor measurement, the system performs automatic calibration of a multi-axis sensor. A reliability of a current calibration is assessed. If the current calibration is reliable, then bias and scale factor values are updated according to the most recent sensor measurement, resulting in updated bias and scale factor values. If the current calibration is not reliable, then previous bias and scale factor values are used. The system causes automatic calibration of the multi-axis sensor using either the updated or previous bias and scale factor values.

Abstract: A microelectromechanical (MEMS) sensor suite including a three axis accelerometer including an accelerometer sensor polyhedron having a series of faces, and a series of axial accelerometers on three faces of the series of faces of the accelerometer sensor polyhedron. The MEMS sensor suite also includes a three axis magnetometer including a magnetometer sensor polyhedron having a series of faces, and a series of axial magnetometers on three faces of the series of faces of the magnetometer sensor polyhedron.

Abstract: A magnetometer comprising a resonating structure which is naturally resonant in at least three resonant modes, a resonant frequency of the three modes being sufficiently separated to allow of detection of same, the resonating structure having two sense electrodes disposed on opposing major surfaces of the resonating structure and having a conductive path formed as a loop, the loop being disposed near or at edges of the resonating structure and the two sense electrodes being formed inwardly of the edges of the resonating structure and also inwardly of the loop.

Abstract: A micro-resonator employs a lid-integrated electrode to one or more of drive, sense and tune a vibrational resonant mode of a microelectromechanical systems (MEMS) resonator. The micro-resonator includes a lid attached to a base that provides a resonator cavity. The micro-resonator further includes the MEMS resonator extending from a surface of the base toward the lid within the resonator cavity. The lid-integrated electrode extends vertically from the lid into the resonator cavity toward the base. The vertically extending, lid-integrated electrode is positioned spaced from and adjacent to a side of the MEMS resonator to one or more of drive, sense and tune mechanical movement of the MEMS resonator.

Abstract: Described is a system for incremental trajectory estimation of an implement. During operation, the system determines a time span of each stationary period of the implement based on accelerometer and gyroscopic data. Gyroscopic bias is then estimated based on the time span and gyroscopic data. An attitude of the implement is then estimated at each time step based on the estimated gyroscopic bias and gyroscopic data. Further, a traveling distance of the implement is estimated. Finally, a trajectory of the implement is estimated based on the estimated attitude and traveling distance. Given the trajectory estimate, an implement (e.g., drilling platform, vehicle, etc.) can be caused to alter its direction based on the trajectory estimate.

Abstract: A magnetometer has a resonating structure which is naturally resonant in at least first and second resonant modes, a resonant frequency of the second mode being at least an order of magnitude greater than a resonant frequency of the first mode, the resonating structure having two sense electrodes disposed on opposing major surfaces of the resonating structure and having a conductive path formed as a loop, the loop being disposed near or at edges of the resonating structure and the two sense electrodes being formed inwardly of the edges of the resonating structure and also inwardly of said loop.

Abstract: Described is a system for estimating a trajectory of a borehole. The system processes signals of sensor streams obtained from an inertial sensor system. Using the set of processed signals, the system determines whether a drill is in a survey mode state or a continuous mode state, and a measured depth of the borehole is determined. A set of survey mode positioning algorithms is applied when the drill is stationary. A set of continuous mode navigation algorithms is applied when the drill is non-stationary. Using at least one Kalman filter, results of the set of survey mode positioning algorithms and the set of continuous mode navigation algorithms are combined. An estimate of a borehole trajectory and corresponding ellipse of uncertainty (EOU) is generated using the combined results.

Abstract: In an embodiment, a tunable stiffness mechanical filter is provided including an input coupler to a negative stiffness structure with a negative stiffness characteristic, and further including a tuner for tuning the negative stiffness structure. An output sensor is located along the negative stiffness structure. The filter may include an amplifier and/or a driver coupled between the output sensor and the negative stiffness structure.

Abstract: A geopositioning system. The geopositioning system includes an accelerometer including three sensing axes, a gyroscope including three sensing axes, and a magnetometer including three sensing axes, and a processing circuit. The processing circuit is configured to calculate a location of the geopositioning system as a latitude, longitude, and altitude with respect to the Earth.

Abstract: A gyroscope includes a cylindrical shell having a first end and a second end, a base on the second end of the shell, a substrate, an anchor coupling the base to the substrate, and electrodes for driving and sensing mechanically separated from the cylindrical shell.

Abstract: A gyroscope including a dielectric resonator, a laser vibrometer on a first side of the dielectric resonator, and a laser dump for redirecting or absorbing light received at the laser dump from the laser vibrometer, the laser dump on a second side of the dielectric resonator. A first distance between the dielectric resonator and the laser vibrometer ranges from 10 nm to 20 ?m, and a second distance between the dielectric resonator and the laser dump ranges from 10 nm to 20 ?m.

Abstract: An apparatus for driving and sensing motion in a gyroscope including a dielectric mass, an anchor, a spring coupled between the anchor and the dielectric mass, a substrate adjacent the dielectric mass, an insulator layer on the substrate, and a first electrode and a second electrode on the insulator layer. When an alternating current voltage is applied between the first and second electrodes, an electric field gradient is generated in the dielectric mass and causes the dielectric mass to move relative to the anchor. When the dielectric mass has motion relative to the anchor and a voltage is applied between the first and second electrodes, the movement of the dielectric mass generates a current at the first and second electrodes proportional to the motion.