Abstract: An inventive accelerometer includes a proof mass and a pair of vibrating sensors. An excitation-and-detection circuit drives one sensor at resonant frequencies f1 and F1, with f1?F1; a second excitation-and-detection circuit drives the other sensor at resonant frequencies f2 and F2, with f2?F2. The vibrational modes driven at the frequencies f1 and f2 are the same for each sensor; the vibrational modes driven at the frequencies F1 and F2 are the same for each sensor. Compressive or tensile loads oppositely applied by the proof mass to the vibrating sensors cause a difference frequency ?F=F1?F2 to vary monotonically with acceleration of the apparatus along a sensing axis, from which a measurement of acceleration can be generated.

Abstract: An inventive accelerometer includes a proof mass, vibrating sensors, and an excitation-and-detection circuit. The vibrating sensors are substantially identical, and each exhibits corresponding fundamental and higher-order vibrational modes characterized by corresponding fundamental and higher-order resonant mode frequencies. The excitation-and-detection circuit drives each corresponding vibrating sensor at one of its resonant mode frequencies f1 or f2; the vibrational modes driven at the frequencies f1 and f2 are the same for each sensor. Compressive or tensile loads oppositely applied by the proof mass to the vibrating sensors cause a difference frequency ?f=f1?f2 to vary monotonically with acceleration of the apparatus along the sensing axis. The excitation-and-detection circuit includes at least one low-pass filter with a low-pass cut-off frequency fLP that is less than ?f.

Abstract: An inventive accelerometer includes a proof mass and a pair of vibrating sensors. Excitation-and-detection circuits drive vibrational modes of one sensor at resonant frequencies f1, F1, and F?1, and drive those same vibrational modes of the other sensor at resonant frequencies f2, F2, and F?2. Compressive or tensile loads oppositely applied by the proof mass to the vibrating sensors cause difference frequencies ?f=f1?f2, ?F=F1?F2, and ?F?=F?1?F?2 to vary monotonically with acceleration of the apparatus along a sensing axis. A measurement of acceleration can be generated based at least in part on a linear or nonlinear function of one or more or all of f1, f2, F1, F2, F?1, or F?2, and can be generated using a trained neural network.

Abstract: An inventive accelerometer includes a proof mass, vibrating sensors, and an excitation-and-detection circuit. The vibrating sensors are substantially identical, and each exhibits corresponding fundamental and higher-order vibrational modes characterized by corresponding fundamental and higher-order resonant mode frequencies. The excitation-and-detection circuit drives each corresponding vibrating sensor at one of its resonant mode frequencies f1 or f2; the vibrational modes driven at the frequencies f1 and f2 are the same for each sensor. Compressive or tensile loads oppositely applied by the proof mass to the vibrating sensors cause a difference frequency ?f=f1?f2 to vary monotonically with acceleration of the apparatus along the sensing axis. The excitation-and-detection circuit includes at least one low-pass filter with a low-pass cut-off frequency fLP that is less than ?f.

Abstract: An inventive accelerometer includes a proof mass and a pair of vibrating sensors. Excitation-and-detection circuits drive vibrational modes of one sensor at resonant frequencies f1, F1, and F?1, and drive those same vibrational modes of the other sensor at resonant frequencies f2, F2, and F?2. Compressive or tensile loads oppositely applied by the proof mass to the vibrating sensors cause difference frequencies ?f=f1?f2, ?F=F1?F2, and ?F?=F?1?F?2 to vary monotonically with acceleration of the apparatus along a sensing axis. A measurement of acceleration can be generated based at least in part on a linear or nonlinear function of one or more or all of f1, f2, F1, F2, F?1, or F?2, and can be generated using a trained neural network.

Abstract: An inventive accelerometer includes a proof mass and a pair of vibrating sensors. An excitation-and-detection circuit drives one sensor at resonant frequencies f1 and F1, with f1?F1; a second excitation-and-detection circuit drives the other sensor at resonant frequencies f2 and F2, with f2?F2. The vibrational modes driven at the frequencies f1 and f2 are the same for each sensor; the vibrational modes driven at the frequencies F1 and F2 are the same for each sensor. Compressive or tensile loads oppositely applied by the proof mass to the vibrating sensors cause a difference frequency ?F=F1?F2 to vary monotonically with acceleration of the apparatus along a sensing axis, from which a measurement of acceleration can be generated.

Abstract: A gyroscope includes at least one anchor and a plurality of gyroscope spring elements coupled to the at least one anchor. The gyroscope also includes a plurality of concentric rings coupled to the plurality of gyroscope spring elements and configured to encircle the plurality of gyroscope spring elements. The gyroscope further includes an excitation/detection/tuning unit electrostatically coupled to the plurality of concentric rings.

Abstract: A gyroscope includes at least one anchor and a plurality of gyroscope spring elements coupled to the at least one anchor. The gyroscope also includes a plurality of concentric rings coupled to the plurality of gyroscope spring elements and configured to encircle the plurality of gyroscope spring elements. The gyroscope further includes an excitation/detection/tuning unit electrostatically coupled to the plurality of concentric rings.

Abstract: A gyroscope includes at least one anchor and a plurality of gyroscope spring elements coupled to the at least one anchor. The gyroscope also includes a plurality of concentric rings coupled to the plurality of gyroscope spring elements and configured to encircle the plurality of gyroscope spring elements. The gyroscope further includes an excitation/detection/tuning unit electrostatically coupled to the plurality of concentric rings.

Abstract: An accelerometer includes a controller, a light source operatively coupled to the controller, and a bifurcated waveguide coupled to the light source and configured to receive light output by the light source. The bifurcated waveguide includes a first waveguide portion and a second waveguide portion. The accelerometer also includes a first resonator operatively coupled to the controller and configured to receive light from the first waveguide portion, and a second resonator operatively coupled to the controller and configured to receive light from the second waveguide portion. The first resonator includes a first proof mass, and the second resonator includes a second proof mass.

Abstract: A method for monitoring a dynamic system includes generating system measurement data substantially representative of at least one measured attribute of a plurality of attributes of a dynamic system using at least one measurement device and generating a Poincare map based on the system measurement data. The Poincare map includes representations of the plurality of attributes of the dynamic system. The method also includes determining at least one value for a first attribute of the plurality of attributes of the dynamic system based on the generated Poincare map and regulating real-time operation of the dynamic system based at least partially on the at least one determined value of the first attribute.

Abstract: An accelerometer includes a controller, a light source operatively coupled to the controller, and a bifurcated waveguide coupled to the light source and configured to receive light output by the light source. The bifurcated waveguide includes a first waveguide portion and a second waveguide portion. The accelerometer also includes a first resonator operatively coupled to the controller and configured to receive light from the first waveguide portion, and a second resonator operatively coupled to the controller and configured to receive light from the second waveguide portion. The first resonator includes a first proof mass, and the second resonator includes a second proof mass.

Abstract: A system and method for electrostatic carouseling for inertial sensor gyrocompassing is disclosed. For performing such electrostatic carouseling for inertial sensor gyrocompassing, a three-rotational degree of freedom spring-mass system is provided that includes a proof mass suspended by a plurality of support springs and having three rotational degrees of freedom, a plurality of driving electrodes, and a controller operably connected to the plurality of driving electrodes. The control applies an excitation voltage to the driving electrodes to generate an electrostatic force, with the controller selectively applying the excitation voltage to the plurality of driving electrodes to generate an electrostatic force that varies an orientation of a gyroscope sensitivity axis for carouseling of the three-rotational degree of freedom spring-mass system.

Abstract: A system and method for electrostatic carouseling for inertial sensor gyrocompassing is disclosed. For performing such electrostatic carouseling for inertial sensor gyrocompassing, a three- rotational degree of freedom spring-mass system is provided that includes a proof mass suspended by a plurality of support springs and having three rotational degrees of freedom, a plurality of driving electrodes, and a controller operably connected to the plurality of driving electrodes. The control applies an excitation voltage to the driving electrodes to generate an electrostatic force, with the controller selectively applying the excitation voltage to the plurality of driving electrodes to generate an electrostatic force that varies an orientation of a gyroscope sensitivity axis for carouseling of the three-rotational degree of freedom spring-mass system.

Abstract: A gyroscope includes at least one anchor and a plurality of gyroscope spring elements coupled to the at least one anchor. The gyroscope also includes a plurality of concentric rings coupled to the plurality of gyroscope spring elements and configured to encircle the plurality of gyroscope spring elements. The gyroscope further includes an excitation/detection/tuning unit electrostatically coupled to the plurality of concentric rings.