Smooth Pursuit Gain

Fit eye velocity against target velocity after caller-supplied saccade/blink exclusions; signed slope and intercept are preserved.

Description

Smooth-pursuit gain can be estimated as the slope relating eye speed to target speed.

Smooth-pursuit gain can be estimated as the slope relating eye speed to target speed. An intercept permits a constant velocity bias.

The tool returns pursuitGain (pursuit gain); velocityBias (velocity bias); rSquared (r squared); usedSamples (used samples). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.

When to use Smooth Pursuit Gain

Use Smooth Pursuit Gain when you already have targetSpeeds, eyeSpeeds, usableFlags and want pursuitGain, velocityBias, rSquared, usedSamples. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.

How to use Smooth Pursuit Gain and understand its results

Enter targetSpeeds, eyeSpeeds, usableFlags using the field table below. Match the units, ordering and data boundaries described in the calculation.
Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
Read pursuitGain, velocityBias, rSquared, usedSamples. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.

Input field	Meaning	Value type and bounds	Requirement
targetSpeeds	Target speeds	list of number	Required
eyeSpeeds	Eye speeds	list of number	Required
usableFlags	Usable flags	list of number	Required

Keep samples whose binary usable flag is one and fit ordinary least squares with an intercept. At least two usable samples with distinct target speeds are needed.

eye speed ≈ bias + gain × target speed

The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.

json

{
  "input": {
    "targetSpeeds": [
      -2,
      -1,
      1,
      2
    ],
    "eyeSpeeds": [
      -1,
      -0.5,
      0.5,
      1
    ],
    "usableFlags": [
      1,
      1,
      1,
      1
    ]
  },
  "output": {
    "pursuitGain": 0.5,
    "velocityBias": 0,
    "rSquared": 1,
    "usedSamples": 4
  }
}

Limitations and assumptions

Sample exclusion is caller-controlled; timing alignment, catch-up saccades and errors in target measurements are not corrected.

Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.

Alternative or Complementary methods

Vestibulo-Ocular Gain: Integrate signed head and eye velocity over a supplied impulse window and compute compensatory area gain; corrective saccades must be excluded by the caller. Saccade Velocity: Derive planar eye-path speeds from timestamped horizontal/vertical angles; finite-difference peaks are cadence-limited and not instantaneous physiological peaks.

Methodological background: Least squares estimation.^[1]

References

Least squares estimation — NIST/SEMATECH

Similar or alternative tools

Vestibulo-Ocular Gain
Integrate signed head and eye velocity over a supplied impulse window and compute compensatory area gain; corrective saccades must be excluded by the caller.
Saccade Velocity
Derive planar eye-path speeds from timestamped horizontal/vertical angles; finite-difference peaks are cadence-limited and not instantaneous physiological peaks.