ossia::kalman_pv_filter Struct Reference

Scalar constant-velocity Kalman filter, one axis of a tracked point. More...

Detailed Description

Scalar constant-velocity Kalman filter, one axis of a tracked point.

State is [position, velocity]; the measurement is the position alone. Velocity is in units per second.

Classes
struct	process_noise
	Discrete process noise covariance for one predict step. More...

Public Member Functions
OSSIA_INLINE void	initiate (float p0, float var_p, float var_v) noexcept
	Start tracking at p0 with the given initial variances.
OSSIA_INLINE void	predict (float dt, const process_noise &q) noexcept
	Propagate the state dt seconds forward.
OSSIA_INLINE void	update (float z, float r) noexcept
	Fold in a position measurement.
OSSIA_INLINE float	gating_distance2 (float z, float r) const noexcept

Static Public Member Functions
static OSSIA_INLINE process_noise	cwna (float sigma_a, float dt) noexcept
	Discretised continuous-white-noise-acceleration process noise.
static OSSIA_INLINE process_noise	diagonal (float std_p, float std_v, float time_ratio) noexcept
	Ad-hoc diagonal process noise, dt-scaled.

Public Attributes
float	p {}
	State: position and velocity (units, units/s).
float	v {}
float	P00 {}
	Covariance, symmetric 2x2: [[P00, P01], [P01, P11]].
float	P01 {}
float	P11 {}

Member Function Documentation

cwna()

static OSSIA_INLINE process_noise ossia::kalman_pv_filter::cwna ( float  sigma_a, float  dt  )

inlinestaticnoexcept

Discretised continuous-white-noise-acceleration process noise.

Q = q * [[dt^3/3, dt^2/2], [dt^2/2, dt]], with q = sigma_a^2.

Parameters

sigma_a	Acceleration magnitude of the tracked motion. Human motion peaks around 2 m/s^2; fitting that as 3 sigma gives ~0.67 as a default in metric spaces. (Strictly q is a power spectral density in units^2/s^3; treating sigma_a^2 as its value is the usual shortcut.)
dt	Time step in seconds.

diagonal()

static OSSIA_INLINE process_noise ossia::kalman_pv_filter::diagonal ( float  std_p, float  std_v, float  time_ratio  )

inlinestaticnoexcept

Ad-hoc diagonal process noise, dt-scaled.

For filters tuned with per-frame standard deviations (ByteTrack's std_weight_position / std_weight_velocity): pass the per-second equivalents and the reference-relative time ratio; reproduces the historical diagonal exactly at the reference rate while still growing with elapsed time.

Parameters

std_p	Position process std for one reference-length step.
std_v	Velocity process std for one reference-length step.
time_ratio	dt / reference_dt.

update()

OSSIA_INLINE void ossia::kalman_pv_filter::update ( float  z, float  r  )

inlinenoexcept

Fold in a position measurement.

Parameters

z	Measured position.
r	Measurement variance (std^2).

gating_distance2()

OSSIA_INLINE float ossia::kalman_pv_filter::gating_distance2 ( float  z, float  r  ) const

inlinenoexcept

Squared Mahalanobis distance of measurement z, in measurement space. Chi-square distributed with 1 DOF; sum over axes for N DOF.