KinematicFeatures

Kinematic feature transformer - velocity, acceleration, curvature.

Takes a discrete N-dimensional space curve, N>=1, and computes a selection of kinematic features.

For noisy time series, is strongly recommended to pipeline this with KalmanFilterTransformerPK or KalmanFilterTransformerFP (prior), or other smoothing or trajectory fitting transformers, as this transformer does not carry out its own smoothing.

For min/max/quantiles of velocity etc, pipeline with SummaryTransformer (post).

For a time series input \(x(t)\), observed at discrete times, this transformer computes (when selected) discretized versions of:

• "v" - vector of velocity: \(\vec{v}(t):= \Delta x(t)\)

• "v_abs" - absolute velocity: \(v(t):= \left| \Delta x(t) \right|\)

• "a" - vector of velocity: \(\vec{a}(t):= \Delta \Delta x(t)\)

• "a_abs" - absolute velocity: \(a(t):= \left| \Delta \Delta x(t) \right|\)

• "curv" - curvature: \(c(t):= \frac{\sqrt{v(t)^2 a(t)^2 - \left\langle \vec{v}(t), \vec{a}(t)\right\rangle^2}}{v(t)^3}\)

where \(\Delta\) denotes first finite differences, that is, \(\Delta z(t) = z(t) - z(t-1)\) for any discrete time series \(z(t)\).

Note: this estimator currently ignores non-equidistant location index, and considers only the integer location index.