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

1. 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;

a sensor configured to generate an output voltage based on a current between the fixed and moveable elements;

comparator circuitry configured to produce an output signal based on detecting the output voltage crossing a threshold;

a time-to-digital converter configured to determine time intervals based on the output signal; and

signal processing circuitry configured to determine an inertial parameter from the time intervals;

wherein monotonic motion of the moveable element relative to the fixed element causes a reversal in direction of the current.

2. The inertial device of claim 1 , wherein the moveable element is springedly coupled to the fixed element.

3. The inertial device of claim 1 , further comprising a drive unit configured to oscillate the moveable element relative to the fixed element.

4. The inertial device of claim 1 , wherein:

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 the reversal in direction of the current.

5. The inertial device of claim 1 , wherein:

the output signal consists essentially of a first value and a second value; and

the comparator circuitry is configured to:

output the first value as the output signal,

receive, from the sensor, the output voltage,

compare a value of the output voltage to the threshold, and

output, based on the comparison, the second value as the output signal.

6. The inertial device of claim 5 , wherein the comparator circuitry is further configured to:

compare the value of the output voltage to a plurality of thresholds;

determine, based on the comparison, that the output voltage crosses one of the plurality of thresholds; and

toggle, based on the determining that the output voltage has crossed one of the plurality of thresholds, the output signal between the first value and the second value.

7. The inertial device of claim 6 , wherein the signal processing circuitry is configured to:

receive the output signal,

determine a time between the toggling of the output signal and a subsequent toggling of the output signal,

based on the determined time, determine the inertial parameter of the inertial device, and

based on the inertial parameter, output an inertial signal.

8. The inertial device of claim 1 , wherein the motion of the moveable element relative to the fixed element is along the second axis.

9. The inertial device of claim 1 , wherein the reversal in direction of the current occurs due to alignment of the first and second pluralities of equally spaced teeth.

10. The inertial device of claim 1 , wherein the reversal in direction of the current occurs due to anti-alignment of the first and second pluralities of equally spaced teeth.

11. The inertial device of claim 1 , wherein each of the first and second pluralities of teeth has a rectangular profile.

12. The inertial device of claim 1 , wherein each of the first and second pluralities of teeth has a non-rectangular profile.

13. The inertial device of claim 1 , further comprising:

a voltage source unit configured to apply a constant voltage to one of 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 current.

14. The inertial device of claim 13 , wherein:

acceleration of the inertial device results in first modulation of the oscillations in the current; and

the first modulation of the oscillations in the current results in second modulation of the output signal.

15. The inertial device of claim 13 , 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.

16. The inertial device of claim 1 , further comprising:

a voltage source unit configured to apply an oscillatory voltage to one of the fixed and moveable elements; and

wherein the oscillatory voltage results in oscillations in the current.

17. The inertial device of claim 16 , wherein:

acceleration of the inertial device results in first modulation of the oscillations in the current; and

the first modulation of the oscillations in the current results in second modulation of the output signal.

18. The inertial device of claim 1 , 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.

19. The inertial device of claim 1 , 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.