Systems and methods for extracting system parameters from nonlinear periodic signals from sensors

Abstract

Systems and methods are disclosed herein for extracting system parameters from nonlinear periodic signals from sensors. A sensor such as an inertial device includes a first structure and a second structure that is springedly coupled to the first structure. The sensor is configured to generate an output voltage based on a current between the first and second structures. Monotonic motion of the second structure relative to the first structure causes a reversal in direction of the current.

1 - 30 . (canceled) 
     
     
         31 . An inertial device, comprising:
 a fixed element comprising a first plurality of beams that are spaced along a first axis;   a first plurality of teeth, adjacent teeth of which are equally spaced along a second axis perpendicular to the first axis, each of the first plurality of teeth disposed on a respective beam of the first plurality of beams;   a moveable element comprising a second plurality of beams that are spaced along the first axis, the moveable element configured to move relative to the fixed element along the second axis;   a second plurality of teeth, adjacent teeth of which are equally spaced along the second axis, each of the second plurality of teeth disposed on a respective beam of the second plurality of beams; and   circuitry configured to:
 generate an output signal based on a capacitance between the fixed and movable elements, 
 determine time intervals based on comparing the output signal to a threshold, and 
 determine an acceleration of the inertial device based on the time intervals. 
   
     
     
         32 . The inertial device of  claim 31 , further comprising:
 a voltage source configured to apply a constant voltage between the fixed and moveable elements; and   a drive unit configured to drive the moveable element in oscillatory motion relative to the fixed element; and   wherein the oscillatory motion of the moveable element relative to the fixed element results in oscillations in the capacitance.   
     
     
         33 . The inertial device of  claim 32 , wherein:
 acceleration of the inertial device results in a first offset in the oscillations in the capacitance; and   the first offset of the oscillations in the capacitance results in changes to the time intervals.   
     
     
         34 . The inertial device of  claim 31 , further comprising:
 a voltage source configured to apply an oscillatory voltage between the fixed and moveable elements;   wherein the oscillatory voltage results in oscillations in the current.   
     
     
         35 . The inertial device of  claim 34 , wherein:
 acceleration of the inertial device results in a first offset in the oscillations in the capacitance; and   the first offset of the oscillations in the capacitance results in changes to the time intervals.   
     
     
         36 . The inertial device of  claim 31 , wherein the moveable element is springedly coupled to the fixed element. 
     
     
         37 . The inertial device of  claim 31 , further comprising a drive unit configured to oscillate the moveable element relative to the fixed element. 
     
     
         38 . The inertial device of  claim 31 , wherein:
 monotonic motion of a first tooth of the first plurality of teeth past an aligned position with a second tooth of the second plurality of teeth causes a nonmonotonic change the capacitance.   
     
     
         39 . The inertial device of  claim 31 , wherein:
 the output signal is a digital signal; and   the circuitry is configured to generate the output signal by:
 determining an analog signal based on the capacitance, 
 comparing the capacitance to a threshold, and 
 changing, based on the comparison, the output signal from a first value to a second value. 
   
     
     
         40 . The inertial device of  claim 39 , wherein the circuitry is further configured to:
 determine, based on comparing the analog signal to a plurality of thresholds, that the analog signal crosses one of the plurality of thresholds; and   change, based on the determining that the output voltage has crossed one of the plurality of thresholds, the output signal from the first value to the second value.   
     
     
         41 . The inertial device of  claim 40 , wherein the circuitry is configured to:
 determine a time between the changing of the output signal and a subsequent changing of the output signal,   based on the determined time, determine the acceleration of the inertial device, and   based on the acceleration, output an acceleration signal.   
     
     
         42 . The inertial device of  claim 31 , wherein the motion of the moveable element relative to the fixed element is along the second axis. 
     
     
         43 . The inertial device of  claim 31 , wherein the nonmonotonic change in capacitance occurs due to alignment of the first and second pluralities of teeth. 
     
     
         44 . The inertial device of  claim 31 , wherein the nonmonotonic change in capacitance occurs due to anti-alignment of the first and second pluralities of teeth. 
     
     
         45 . The inertial device of  claim 32 , wherein the drive unit is further configured to:
 receive the output signal; and   based on the received output signal, adjust the oscillatory motion of the moveable element relative to the fixed element.   
     
     
         46 . The inertial device of  claim 31 , wherein:
 centers of adjacent teeth of the first plurality of teeth are separated by a first pitch distance; and   centers of adjacent teeth of the second plurality of teeth are separated by the first pitch distance.   
     
     
         47 . The inertial device of  claim 31 , wherein:
 centers of adjacent beams of the first plurality of beams are separated by a second pitch distance; and   centers of adjacent beams of the second plurality of beams are separated by the second pitch distance.   
     
     
         48 . A method, comprising:
 generating an output signal based on a capacitance between the fixed and movable elements, wherein:
 the fixed element comprises a first plurality of beams that are spaced along a first axis and a first plurality of teeth, adjacent teeth of which are equally spaced along a second axis perpendicular to the first axis, each of the first plurality of teeth disposed on a respective beam of the first plurality of beams, 
 the moveable element comprises a second plurality of beams that are spaced along the first axis, the moveable element configured to move relative to the fixed element along the second axis, and a second plurality of teeth, adjacent teeth of which are equally spaced along the second axis, each of the second plurality of teeth disposed on a respective beam of the second plurality of beams, and 
   determining time intervals based on comparing the output signal to a threshold; and   determining an acceleration of the method based on the time intervals.   
     
     
         49 . The method of  claim 48 , further comprising:
 applying a constant voltage between the fixed and moveable elements; and   driving the moveable element in oscillatory motion relative to the fixed element; and   wherein the oscillatory motion of the moveable element relative to the fixed element results in oscillations in the capacitance.   
     
     
         50 . The method of  claim 49 , wherein:
 acceleration of the method results in a first offset in the oscillations in the capacitance; and   the first offset of the oscillations in the capacitance results in changes to the time intervals.   
     
     
         51 . The method of  claim 48 , further comprising:
 applying an oscillatory voltage between the fixed and moveable elements;   wherein the oscillatory voltage results in oscillations in the current.   
     
     
         52 . The method of  claim 51 , wherein:
 acceleration of the method results in a first offset in the oscillations in the capacitance; and   the first offset of the oscillations in the capacitance results in changes to the time intervals.   
     
     
         53 . The method of  claim 48 , wherein the moveable element is springedly coupled to the fixed element. 
     
     
         54 . The method of  claim 48 , further comprising oscillating the moveable element relative to the fixed element. 
     
     
         55 . The method of  claim 48 , wherein:
 monotonic motion of a first tooth of the first plurality of teeth past an aligned position with a second tooth of the second plurality of teeth causes a nonmonotonic change the capacitance.   
     
     
         56 . The method of  claim 48 , wherein
 the output signal is a digital signal; and   generating the output signal comprises:
 determining an analog signal based on the capacitance, 
 comparing the capacitance to a threshold, and 
 changing, based on the comparison, the output signal from a first value to a second value. 
   
     
     
         57 . The method of  claim 56 , further comprising:
 determining, based on comparing the analog signal to a plurality of thresholds, that the analog signal crosses one of the plurality of thresholds; and   changing, based on the determining that the output voltage has crossed one of the plurality of thresholds, the output signal from the first value to the second value.   
     
     
         58 . The method of  claim 57 , further comprising:
 determining a time between the changing of the output signal and a subsequent changing of the output signal,   based on the determined time, determining the acceleration of the method, and   based on the acceleration, outputting an acceleration signal.   
     
     
         59 . The method of  claim 48 , wherein the motion of the moveable element relative to the fixed element is along the second axis. 
     
     
         60 . The method of  claim 48 , wherein the nonmonotonic change in capacitance occurs due to alignment of the first and second pluralities of teeth. 
     
     
         61 . The method of  claim 48 , wherein the nonmonotonic change in capacitance occurs due to anti-alignment of the first and second pluralities of teeth. 
     
     
         62 . The method of  claim 49 , further comprising adjusting, based on the received output signal, the oscillatory motion of the moveable element relative to the fixed element. 
     
     
         63 . The method of  claim 48 , wherein:
 centers of adjacent teeth of the first plurality of teeth are separated by a first pitch distance; and   centers of adjacent teeth of the second plurality of teeth are separated by the first pitch distance.   
     
     
         64 . The method of  claim 48 , wherein:
 centers of adjacent beams of the first plurality of beams are separated by a second pitch distance; and   centers of adjacent beams of the second plurality of beams are separated by the second pitch distance.