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 vapor-cell system and method is provided, comprising an enclosed vapor-cell region containing a vapor-cell gas phase comprising a vapor-cell alkali or alkaline earth metal, wherein the vapor-cell region is configured to allow at least one vapor-cell optical path through the vapor-cell gas phase; an enclosed reservoir region containing a reservoir alkali or alkaline earth metal, wherein the reservoir region is in vapor isolation from the vapor-cell region; a solid electrolyte disposed in ionic communication between the vapor-cell region and the reservoir region; a first electrode disposed between the solid electrolyte and the vapor-cell region; and a second electrode disposed between the solid electrolyte and the reservoir region, wherein the second electrode is electrically isolated from the first electrode. This vapor-cell system enables independent control of the alkali or alkaline earth vapor pressure in the vapor cell.

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: 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: Described is a system for position estimation. A set of raw sensor outputs are acquired from a sensor of a platform. The set of raw sensor outputs are stored in non-transitory memory. A set of optimized sensor measurements is generated by deducing errors in the raw sensor outputs using an unconstrained optimization algorithm. The system determines a position of the platform based on the set of optimized sensor measurements.

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: In some variations, a vapor-cell system comprises: a vapor-cell region configured to allow at least one vapor-cell optical path into a vapor phase within the vapor-cell region; a first electrode disposed in contact with the vapor-cell region; a second electrode that is electrically isolated from the first electrode; and a transparent ion-conducting layer interposed between the first electrode and the second electrode, wherein the transparent ion-conducting layer is optically transparent over a selected optical band of electromagnetic wavelengths. Some embodiments provide a magneto-optical trap or atomic-cloud imaging apparatus, comprising: the disclosed vapor-cell system; a source of laser beams configured to provide three orthogonal vapor-cell optical paths through the vapor-cell gas phase, to trap or image a population of cold atoms; and a magnetic-field source configured to generate magnetic fields within the vapor-cell region. Methods of use are also disclosed herein.

Abstract: Microelectromechanical resonators include a resonator body anchored to a surrounding substrate by at least one support that holds the resonator body opposite a recess in the substrate. The resonator body has first and second pluralities of interdigitated drive and sense electrodes thereon. The first plurality of interdigitated drive and second electrodes are aligned to a first axis of acoustic wave propagation in the resonator body when the resonator body is operating at resonance. In contrast, the second plurality of interdigitated drive and sense electrodes are aligned to a second axis of acoustic wave propagation in the resonator body. This second axis of acoustic wave propagation preferably extends at an angle in a range from 60° to 120° relative to the first axis and, more preferably, at an angle of 90° relative to the first axis.

Abstract: A micro-electromechanical resonator self-compensates for process-induced dimensional variations by using a resonator body having a plurality of perforations therein. These perforations may be spaced along a longitudinal axis of the resonator body, which extends orthogonal to a nodal line of the resonator body. These perforations, which may be square or similarly-shaped polygonal slots, may extend partially or entirely though the resonator body and may be defined by the same processes that are used to define the outer dimensions (e.g., length, width) of the resonator body.

Abstract: A micro-electromechanical resonator self-compensates for process-induced dimensional variations by using a resonator body having a plurality of perforations therein. These perforations may be spaced along a longitudinal axis of the resonator body, which extends orthogonal to a nodal line of the resonator body. These perforations, which may be square or similarly-shaped polygonal slots, may extend partially or entirely though the resonator body and may be defined by the same processes that are used to define the outer dimensions (e.g., length, width) of the resonator body.