Abstract: A method and apparatus for for sensing a change in an acceleration gradient ?a(t) between two gravity fields a1(t) and a2(t) respectively sensed by the first and second proof masses, the first and second proof masses either being coupled only to a first resonator or being individually coupled to first and second resonators, the first resonator generating, in use, a signal at a frequency fD which is applied said second resonator, the second resonator being driven, in use, into a non-linear state corresponding to a modal resonant frequency f? wherein it generates a comb of frequencies each tooth of which is separated from each other by a frequency ? which is frequency-wise proportional a frequency difference between fD and f? and also proportional to the change in said acceleration gradient ?a(t), circuitry for selecting an nth tooth in said comb of frequencies where the frequency of the nth tooth is equal to fD+n?, circuitry for detecting a change in the frequency of the nth tooth and for generating a signal t

Abstract: An angular rate sensor. The sensor includes a Coriolis vibratory gyroscope (CVG) resonator, configured to oscillate in a first normal mode and in a second normal mode; a frequency reference configured to generate a reference signal; and a first phase control circuit. The first phase control circuit is configured to: measure a first phase difference between: a first phase target, and the difference between: a phase of an oscillation of the first normal mode and a phase of the reference signal. The first phase control circuit is further configured to apply a first phase correction signal to the CVG resonator, to reduce the first phase difference. A second phase control circuit is similarly configured to apply a second phase correction signal to the CVG resonator, to reduce a corresponding, second phase difference.

Abstract: A resonator has a resonator body and a frame at least partially surrounding the resonator body, the resonator body being coupled to the frame by at least one tether. The resonator body, frame and at least one tether comprise silicon carbide. A plurality of interdigitated electrodes are disposed on the silicon carbide resonator body. The resonator body preferably comprises 6H silicon carbide and preferably has a crystalline c-axis oriented generally parallel to a thickness direction of the resonator body.

Abstract: A self-calibration method for an accelerometer having a proof mass separated by a gap from a drive electrode and a sense electrode includes initializing the accelerometer to resonate, applying a first bias voltage to the sense electrode and a second bias voltage to the drive electrode to obtain a first scale factor, measuring a first acceleration over a first time interval, swapping the first bias voltage on the sense electrode with the second bias voltage previously on the drive electrode and the second bias voltage on the drive electrode with the first bias voltage previously on the sense electrode so that a bias voltage on the sense electrode is set to the second bias voltage and a bias voltage on the drive electrode is set to the second bias voltage to obtain a second scale factor, measuring a second acceleration over a second time interval, and calculating a true acceleration.

Abstract: A method of making a SiC resonator includes forming a layer of an oxide material on a relatively thick wafer of SiC; bonding the layer of oxide material on the relatively thick wafer of SiC to a handle wafer having at least an oxide exterior surface, the resulting bond being substantially free of voids; planarizing the relatively thick wafer of SiC to a desired thickness; forming top and bottom electrodes on the wafer of SiC wafer to define a SiC wafer resonator portion; and forming a trench around the top and bottom electrodes, the tench completely penetrating the planarized wafer of SiC around a majority of a distance surrounding said top and bottom electrodes, except for one or more tether regions of the planarized wafer of SiC which remain physically coupled a remaining portion the SiC wafer resonator portion which defines a frame formed of the planarized wafer of SiC surrounding the SiC wafer resonator portion.

Abstract: A stress isolating interposer includes: an outer pad; an inner pad configured to accommodate a positional sensor is mounted; and a stress isolating structure coupling the outer pad and the inner pad to each other. The outer pad, the stress isolating structure, and the inner pad are a monolithic structure.

Abstract: An instrument package for use during the drilling a wellbore. The instrument package includes a plurality of instruments such as accelerometers, gyroscopes, and magnetometers; a computer is configured to determine the current position of the plurality of instruments from a set of measurements produced by the plurality of instruments; and wherein the plurality of instruments are mechanically isolated from a drill head assembly by one or more multi-degree of freedom vibration isolators. The computer preferably has at least two modes different analytical modes of analyzing the set of measurements produced by the plurality of instruments, including a continuous mode and a survey mode, the continuous mode being operational during times that active drilling is occurring and the survey mode being operational during times that the active drilling is not occurring.

Abstract: A resonant accelerometer includes a proof mass, one or more springs connecting the proof mass to an anchor, and one or more capacitive transduction gaps providing a void or space between the movable proof mass and a corresponding fixed electrode, wherein the static displacement of the proof mass in response to acceleration applied to the anchor modifies the electrostatic stiffness imparted by one or more of the capacitive transduction gaps on the proof mass, resulting in a corresponding change in the resonance frequency of the resonant accelerometer.

Abstract: A curved phononic waveguide. In some embodiments, the curved phononic waveguide includes a sheet including a plurality of standard reflectors and a plurality of divergent reflectors. Each of the standard reflectors is associated with a respective grid point of a grid defined by a plurality of intersecting lines, each grid point being a respective intersection of two of a plurality of intersecting lines, the grid being locally periodic to within 5%, and having a local grid spacing. Each of the standard reflectors has a center separated from the respective grid point of the standard reflector by at most 1% of the grid spacing. The divergent reflectors define a waveguide among the standard reflectors, each of the divergent reflectors being an absent reflector or a reflector that is smaller than one of the standard reflectors.

Abstract: A sensor comprising a resonator structure arranged for resonating along a first plane; and at least one sensing electrode arranged on a second plane parallel to said first plane at a predetermined distance of said resonator structure along a direction normal to said first plane.

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: 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 phononic coupler. In some embodiments, the phononic coupler includes a sheet, including a plurality of standard reflectors, and a plurality of divergent reflectors. The divergent reflectors define, among the standard reflectors, a first waveguide, and a second waveguide. The coupler has a first port, at a first end of the coupler, a second port, at the first end of the coupler, and a third port, at a second end of the coupler. The first waveguide has a first end at the first port. The second waveguide has a first end at the second port, and a second end at the third port. The coupler is configured to couple longitudinal sound waves to both the first port and the second port.

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: Dimensions of a disk resonator gyroscope along the radial line of a resonator can be varied to engineer radial stiffness. An apparatus may comprise: a resonator comprising a plurality of concentric circumferential segments and a plurality of slots formed between the concentric circumferential segments; and at least one support supporting the resonator, wherein a width, in a radial direction, of each of the concentric circumferential segments is varied depending on a distance from the at least one support to the each of the concentric circumferential segments. The apparatus may further comprise radial segments connecting between the concentric circumferential segments. The concentric circumferential segments may have a ring shape.

Abstract: A sensor includes an acceleration or magnetic field sensitive microelectromechanical systems (MEMS) resonator, configured to oscillate in at least a first normal mode and a second normal mode. The sensor further includes: a coarse readout circuit configured to drive the first normal mode, measure a motion of the first normal mode, and derive from the measured motion a coarse measurement of the true acceleration or true external magnetic field; and a fine readout circuit configured to drive the second normal mode, measure a motion of the second normal mode, and derive from the measured motion and the coarse measurement a measurement of the difference between the true acceleration or true external magnetic field and the coarse measurement.

Abstract: Some variations provide an alkali metal or alkaline earth metal vapor cell with a solid ionic conductor and intercalable-compound electrodes. The intercalable-compound electrodes are used as efficient sources and/or as sinks for alkali metal or alkaline earth metal atoms, thus enabling electrical control over metal atom content in the vapor cell. Some variations provide a vapor-cell system comprising: a vapor-cell region configured to allow a vapor-cell optical path into a vapor-cell vapor phase; a first electrode; a second electrode electrically isolated from the first electrode, wherein the second electrode contains an intercalable compound intercalated by an element selected from Rb, Cs, Na, K, or Sr; and an ion-conducting layer between the first electrode and the second electrode. The ion-conducting layer is ionically conductive for at least one ionic species selected from Rb+, Cs+, Na+, K+, or Sr2+. The intercalable compound is preferably a carbonaceous material, such as graphite.

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: 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: A sensor includes an acceleration or magnetic field sensitive microelectromechanical systems (MEMS) resonator, configured to oscillate in at least a first normal mode and a second normal mode. The sensor further includes: a coarse readout circuit configured to drive the first normal mode, measure a motion of the first normal mode, and derive from the measured motion a coarse measurement of the true acceleration or true external magnetic field; and a fine readout circuit configured to drive the second normal mode, measure a motion of the second normal mode, and derive from the measured motion and the coarse measurement a measurement of the difference between the true acceleration or true external magnetic field and the coarse measurement.