SYSTEMS AND METHODS FOR EXTRACTING SYSTEM PARAMETERS FROM NONLINEAR PERIODIC SIGNALS FROM SENSORS

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.