SYSTEMS AND METHODS FOR MULTI-TIER CENTROID CALCULATION
Described herein are systems and methods that determines a centroid of a waveform in a high noise environment. In one embodiment, the method may include determining a damping threshold and a noise-exclusion threshold for a waveform that define a three tier dynamic range for the waveform comprising a noise-exclusion region, damping region and a full region. The noise-exclusion threshold may be less than the damping threshold. Weights for each of the mass scalars may be determined based on the three tier dynamic range. The centroid may be determined based on the determined weights and their corresponding position vectors.
1 . An apparatus comprising:
a threshold defining circuitry operable to determine a noise-exclusion threshold and a damping threshold for a waveform, wherein the noise-exclusion threshold is less than the damping threshold;
a weight calculation circuitry operable to determine weights of mass scalars of the waveform based on the noise-exclusion threshold, the damping threshold and mass scalar values; and
a centroid calculation circuitry operable to determine a centroid of the waveform based on determined weights of mass scalars and their corresponding position vectors.
2 . The apparatus of claim 1 , wherein,
the centroid of the waveform comprises a sum of a multiplication of an i-th position vector and a determined weight of an i-th mass scalar, divided by the sum of the determined weights of the mass scalars.
3 . The apparatus of claim 1 , wherein,
if an i-th mass scalar is less than the damping threshold, but greater than the noise-exclusion threshold, a determined weight of the i-th mass scalars is equal to a difference between the i-th mass scalar and the noise-exclusion threshold, divided by a difference between the damping threshold and the noise-exclusion threshold.
4 . The apparatus of claim 1 , wherein,
if an i-th mass scalar is greater than the damping threshold, a determined weight of the i-th mass scalar is equal to a value of the i-th mass scalar.
5 . The apparatus of claim 1 , wherein,
if an i-th mass scalar is less than the noise-exclusion threshold, a determined weight of the i-th mass scalar is equal to zero.
6 . The apparatus of claim 1 , wherein,
a damping region comprises mass scalars having values greater than the noise-exclusion threshold and less than the damping threshold,
a full region comprises mass scalars having values greater than the damping threshold, and
a noise-exclusion region comprises mass scalar having values less than the damping threshold.
7 . The apparatus of claim 6 , wherein,
the mass scalars of the waveform located in the full region have a greater S/N ratio than the mass scalars of the waveform located in the damping region.
8 . The apparatus of claim 6 , wherein,
the mass scalars of the waveform located in the damping region have a greater S/N ratio than the mass scalars of the waveform located in the noise-exclusion region.
9 . A method comprising:
determining, at a centroid apparatus, a damping threshold and a noise-exclusion threshold for a waveform that define a three tier dynamic range for the waveform comprising a noise-exclusion region, a damping region and a full region, wherein the noise-exclusion threshold is less than the damping threshold;
determining, at the centroid apparatus, weights for each of mass scalars of the waveform based on the three tier dynamic range; and
determining, at the centroid apparatus, a centroid based on the determined weights and their corresponding position vectors.
10 . The method of claim 9 , wherein,
the centroid of the waveform comprises a sum of a multiplication of an i-th position vector of and a determined weight of an i-th mass scalar, divided by a sum of the determined weights of the mass scalars.
11 . The method of claim 9 , wherein,
if an i-th mass scalar is less than the damping threshold, but greater than the noise-exclusion threshold, a determined weight of the i-th mass scalar is equal to a difference between the i-th mass scalar and the noise-exclusion threshold, divided by the difference between the damping threshold and the noise-exclusion threshold.
12 . The method of claim 9 , wherein,
if an i-th mass scalar is greater than the damping threshold, a determined weight of the i-th mass scalar is equal to the i-th mass scalar.
13 . The method of claim 9 , wherein,
if an i-th mass scalar is less than the noise-exclusion threshold, a determined weight of the i-th mass scalar is equal to zero.
14 . The method of claim 9 , wherein,
the damping region comprises mass scalars having values greater than the noise-exclusion threshold and less than the damping threshold,
the full region comprises mass scalars having values greater than the damping threshold, and
the noise-exclusion region comprises mass scalars having values less than the damping threshold.
15 . The method of claim 9 , wherein,
the mass scalars of the waveform located in the full region have a greater S/N ratio than the mass scalars of the waveform located in the damping region.
16 . The method of claim 9 , wherein,
the mass scalars of the waveform located in the damping region have a greater S/N ratio than the mass scalars of the waveform located in the noise-exclusion region.
17 . The method of claim 9 , wherein, the damping threshold and the noise-exclusion threshold for the waveform are dynamically adjusted while determining the centroid.
18 . A non-transitory computer readable storage medium having computer program code stored thereon, the computer program code, when executed by one or more processors implemented on an centroid apparatus, causes the centroid apparatus to perform a method comprising:
determining a damping threshold and a noise-exclusion threshold for a waveform that define a three tier dynamic range for the waveform comprising a noise-exclusion region, damping region and a full region, wherein the noise-exclusion threshold is less than the damping threshold;
determining weights for each of mass scalars of the waveform based on the three tier dynamic range; and
determining, a centroid based on the determined weights and their corresponding position vectors.
19 . The method of claim 18 , wherein,
the centroid of the waveform comprises a sum of a multiplication of an i-th position vector and a determined weight of an i-th mass scalar, divided by the sum of the determined weights of the mass scalars.
20 . The method of claim 18 , wherein, the damping threshold and the noise-exclusion threshold for the waveform are dynamically adjusted while determining the centroid.