15.116 14.5.7 Filtrado y derivación
Savitzky–Golay formaliza un ajuste polinomial local que puede suavizar y diferenciar una serie [P45-R7]. Sin embargo, ningún filtro posee parámetros universales para todos los joints, cámaras, FPS o movimientos.
| Perfil | Modo | Parámetros | Orden derivable | Uso |
|---|---|---|---|---|
FILTER-NONE |
None | {} | 0 | Raw display and audit only. |
FILTER-SG-OFFLINE |
SavitzkyGolay | {“windowSamples”: “odd, tuned”, “polynomialOrder”: “2..4”, “edgeMode”: “declared”} | 3 | Offline local polynomial smoothing/differentiation. |
FILTER-BUTTER-ZP |
ZeroPhaseButterworth | {“order”: “declared”, “cutoffHz”: “validated”, “padding”: “declared”} | 2 | Offline low-pass when zero-phase processing is acceptable. |
FILTER-SPLINE |
SmoothingSpline | {“loss”: “L2|robust”, “regularization”: “validated”} | 3 | Irregular samples and analytic derivatives. |
FILTER-KALMAN-RTS |
StateSpaceSmoother | {“motionModel”: “declared”, “processNoise”: “estimated”, “measurementCovariance”: “from pose/depth”} | 2 | Fusion and uncertainty-aware offline smoothing. |
FILTER-KALMAN-CAUSAL |
CausalStateSpace | {“latencyMs”: “declared”} | 2 | Online provisional features. |
15.116.1 Perfiles de derivada
| Perfil | Método | Órdenes | Bordes | Requisitos |
|---|---|---|---|---|
DERIV-CENTRAL |
Central finite difference on uniform samples | 1, 2 | invalidate or one-sided flagged | uniform dt and prior filtering |
DERIV-SG |
Savitzky-Golay derivative coefficients | 1, 2, 3 | declared interpolation/padding | window and polynomial order compatible |
DERIV-SPLINE |
Analytic derivative of fitted spline | 1, 2, 3 | confidence expands near boundaries | regularization and knot policy |
DERIV-STATE |
Velocity/acceleration from state-space posterior | 1, 2 | posterior covariance retained | validated dynamics model |
DERIV-SO3 |
Rotation-log finite difference or spline on SO(3) | 1, 2 | unwrap/continuity and invalid large jumps | valid orientation sequence |
v(t) = dp/dt
a(t) = d²p/dt²
j(t) = d³p/dt³Cada orden amplifica el ruido y reduce la región válida cerca de bordes o huecos. Por ello la confianza de posición no puede copiarse sin cambio a velocidad, aceleración o jerk.